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BRIDGE 


AND 


TUNNEL  CENTRES. 


JOHN  B.  McMASTEE,  0.  E. 


OF  THB 

TJHI7ER 


YORK: 

D.  VAN  NOSTRAND,  PUBLISHER, 

23  MURRAY  AND  2T  WABREN  STREET. 

1875. 


Page  77,  lines  4  and  7  from  bottom,  and 
78'     "2-6     "      top,          for 
yard  read  foot. 


nor  is  it  intended  to  furnish  a  variety  of  designs 
likely  to  be  useful  to  the  carpenter  and  bridge- 
builder  ;  it  does  not  claim  to  be  analytical  ;  it 
is  purely  practical. 

Very  much,  therefore,  of  what,  under  other 
circumstances,  might  most  fittingly  have  been 
introduced,  has  been  carefully  omitted,  and 
nothing  set  down  which  does  not  bear  directly 


<0 


Y 


It  is  the  purpose  of  the  following  essay  to 
present  in  as  brief  a  manner  as  the  nature  of 
the  subject  will  allow,  the  rules  and  principles, 
the  application  and  observance  of  which  is  of 
really  vital  importance  in  the  planning  and  con- 
struction of  Bridge  and  Tunnel  Centring.  It 
is  not  offered  as  a  highly  elaborated  and  ex- 
haustive treatise  on  this  branch  of  engineering, 
nor  is  it  intended  to  furnish  a  variety  of  designs 
likely  to  be  useful  to  the  carpenter  and  bridge  - 
builder  ;  it  does  not  claim  to  be  analytical  ;  it 
is  purely  practical. 

Very  much,  therefore,  of  what,  under  other 
circumstances,  might  most  fittingly  have  been 
introduced,  has  been  carefully  omitted,  and 
nothing  set  down  which  does  not  bear  directly 


on  the  subject  in  hand,  and  had  not  been  veri- 
fied, time  and  again,  by  actual  experiment.  It 
will  be  observed,  for  instance,  that  what  may 
be  termed  the  mathematics  of  the  subject  finds 
no  place  here.  There  are  no  mathematical  de- 
monstrations, no  lengthy  discussions  of  the 
various  formulae  introduced  ;  they  are  simply 
set  down  as  expressing  established  truths,  the 
proof  of  their  correctness  in  many  cases  sup- 
pressed, and  the  reader  requested  to  accept 
them  as  true.  In  the  form  in  which  this  essay 
first  appeared,  this  was  done  to  save  space  ;  in 
the  present  form  it  has  been  strictly  adhered 
to,  because  it  is  believed  that  those  to  whom 
the  work  will  be  of  the  most  use,  are  precisely 
those  who  will  be  content  to  take  as  true  the 
formulae  given,  caring  very  little  for  the  steps 
by  which  it  has  been  reached. 

In  connection  with  the  matter  of  estimating 
the  load  on  a  centre,  four  methods  have  been 
selected,  either  of  which  will  give  results  close 
enough  to  the  absolute  truth  for  all  practical 
purposes.  The  first,  that  of  M.  Couplet,  is 
extremely  simple^  and  if  it  errs  at  all,  does  so 
on  the  side  of  safety.  The  second  or  "  graphic- 


al"  is  constantly  growing  in  favor,  and  most 
deservedly  so  ;  the  third,  that  by  calculus,  dis- 
regards friction  and  give  results  greatly  in  ex- 
cess of  the  truth,  while  the  fourth,  or  trigono- 
metrical, is  perhaps  the  most  exact  of  all,  and 
admits  the  application  of  logarithms. 

The  remarks  on  the  subject  of  uncentring  are 
believed  to  be  sufficiently  extended,  though  the 
subject  is  one  of  great  importance.  The  prin- 
ciples, however,  to  be  observed  in  striking 
centres  are  quite  few  and  simple,  the  observance 
being  all  that  is  necessary  to  secure  success. 
The  sand  method  cannot  be  too  highly  com- 
mended. 

The  remarks  coming  under  the  head  of  tun- 
nel centres,  have  been  limited  to  pointing  out 
the  essential  difference  between  the  centre 
proper  for  bridging,  and  that  suitable  for  tun- 
nelling, to  calling  attention  to  the  peculiar 
variability  of  the  strains,  and  to  the  care  to  be 
observed  in  guarding  against  the  accidents  so 
liable  to  produce  injury  to  the  ribs,  and  to  of- 
fering a  few  practical  suggestions  as  to  econo- 
my. A  few  designs  have  also  been  added  as 
illustrative  of  the  principles  1  aid  down,  and  as 


6 

affording  examples  of  cheap  and  durable 
frames.  The  patent  centre  of  Mr.  Frazer  is 
worthy  of  some  attention. 

JOHN  B.  McMASTER. 
NEW  YORK,  November,  1875. 


BRIDGE  AND  TUNNEL  CENTRES. 


IN  the  construction  of  stone  and  brick 
arches,  of  whatever  shape  and  span,  and 
to  whatever  use  applied,  whether  as  sup- 
ports for  roadways  or  roofs  of  tunnels, 
there  is  nothing  which  requires  more 
careful  attention  on  the  part  of  the  con- 
structing engineer,  than  the  centres. 
Independent  of  the  choice  of  material, 
of  the  exactness  with  which  each  stone 
is  cut,  and  the  care  with  which  it  is  laid 
in  place,  the  success  of  arches  of  great 
span,  their  settlement  and  ultimate  sta- 
bility depends  essentially  on  the  care 
given  to  the  framing,  setting  up  and 
striking  of  the  centres.  The  slightest 
change  in  the  shape  of  the  frame  caused 
by  the  shrinking  of  an  ill-seasoned  tim- 


8 

ber,  or  the  yielding  to  compression  of  a 
badly  proportioned  brace,  will  assuredly 
be  followed  by  a  change  in  the  curve  of 
the  intrados,  which  may  possibly  result 
in  the  ruin  of  the  arch  itself. 

Well  constructed  centring,  therefore, 
is  indispensably  necessary  to  a  well  con- 
structed arch,  and  in  the  following  papers 
it  is  our  intention  to  offer  a  practical  in- 
vestigation of  the  principles  which  must 
be  followed  out  in  the  planning  and  me- 
chanical execution  of  all  such  centre 
frames  ;  to  determine  wKat  strains  must 
be  withstood,  at  what  point  they  act 
with  most  vigor,  and  by  what  combina- 
tion of  beams  and  by  what  system  of 
bracing,  the  greatest  strength  and  stiff- 
ness may  be  combined  with  the  utmost 
lightness  and  the  strictest  economy  of 
material. 

BRIDGE    CENTRES. 

Of  all  classes  of  centres,  the  most  com- 
plicated in  structure  is,  beyond  doubt, 
that  of  a  large  span  stone  bridge.  Like 
a  roof  frame,  it  consists  of  a  number  of 
vertical  pieces,  placed  in  the  direction  of 


9 

the  span,  from  5  to  7  ft.  from  centre  to 
centre,  and  known  as  the  ribs,  upon  which 
are  placed  horizontal  pieces  or  laggings, 
and  on  these  latter  rest  the  voussoirs  till 
the  key  stone  course  is  driven  and  the 
arch  becomes  self-supporting. 

THE  FKAME  in  its  turn  is  composed  of 
back  pieces,  or  short  beams  cut  on  the 
outer  edge  to  the  same  curve  as  the  in- 
trados  of  the  arch,  a  horizontal  tie  beam, 
and  a  number  of  struts,  ties  and  braces,  the 
arrangement,  number  and  dimensions  of 
which,  will  depend  on  the  shape  and  span 
of  the  arch,  and  the  number  and  position 
of  the  points  of  support.  Whatever  may 
be  the  span  and  curve  of  the  arch,  and  the 
points  of  support  afforded,  experience 
has  amply  proved  that  the  ribs  should  be 
polygonal  in  shape,  with  short  sides  ; 
this  shape  being  given  by  forming  the 
back-pieces,  on  which  rest  the  laggings, 
of  two  or  more  courses  of  planks,  placed 
in  the  form  of  a  polygon  and  firmly  nail- 
ed together  ;  the  planks  in  each  course 
abutting  end  to  end  by  a  joint  in  the  di- 
rection of  the  radius  of  curvature  of  the 


JO 

arch,  and  breaking  joints  with  those  of 
the  other  course. 

For  light  arches  of  moderate  span,  or 
indeed  for  heavy  arches  of  wide  span 
when  firm  intermediate  points  of  sup- 
port can  be  had  between  the  abutments, 
the  back  pieces  may  be  strengthened  by 
struts  or  ties  placed  under  them,  well 
braced,  and  abutting  against  a  horizon- 
tal tie  beam.  This  beam  spans  the  arch 
a  little  above  the  springing  line,  is  bolt- 
ed to  the  back-pieces  at  either  side,  thus 
preventing  them  from  spreading  later- 
ally, and  if  well  sustained  by  props  from 
beneath,  affords  a  firm  support  to  the 
struts  and  braces  of  the  rib.  In  by  far 
the  greater  number  of  cases,  however, 
where  headway  is  required  under  the 
centring  during  the  construction  of  the 
arch,  as  is  the  case  with  stone  bridges 
spanning  a  river  whose  navigation  can- 
not be  impeded,  or  whose  current  is  too 
swift  and  depth  too  great  to  give  firm 
points  of  support  to  the  props  of  the 
tie  beam,  it  becomes  necessary  to  do 
away  with  the  latter,  and  supply  its  place 


11 

by  such  an  arrangement  of  beams  as  will 
transmit  the  strains  received  to  points 
of  support  at  the  abutments.  This  lat- 
ter class  of  centring  is  known  as  "re- 
troussee"  or  " cocket"  and  requires  a 
much  more  careful  and  elaborate  arrange- 
ment of  its  parts  than  the  former. 

We  have  therefore  two  classes  of 
bridge  centres  to  deal  with  ;  one  in 
which  the  frame  is  constructed  without 
regard  to  headway  beneath  it,  and  is 
supported  from  firm  points  of  support 
between  the  abutments,  and  one  arrang- 
ed to  leave  headway  under  the  frame, 
and  upheld  by  framed  supports  at  the 
abutments. 

Before  attempting  to  determine  the 
most  advantageous  arrangement  of  the 
pieces  which  must  compose  the  frame, 
their  number  and  the  dimensions  it  is 
necessary  to  give  them  in  order  that  they 
may  offer  a  solid  support  to  the  arch 
stones,  it  is  fitting  to  consider  the  effect 
of  the  load  the  ribs  are  expected  to  up- 
hold, the  strains  it  produces,  the  points 
where  and  the  directions  in  which  the 
strains  act  and  their  intensity. 


12 


THE   STRAINS. 

The  strains  to  which  centre  frames  are 
subjected  arise  solely  from  the  pressure 
upon  the  back-pieces  and  laggings,  due 
to  the  weight  of  the  voussoirs  laid  upon 
them,  and  are  therefore  extremely  vari- 
able, depending  on  the  span  and  curve 
of  the  arch,  and  the  thickness  and  weight 
per  cubic  foot  of  the  voussoirs  which 
press  upon  the  centring.  It  is  not, 
however,  to  be  supposed  that  all  the 
voussoirs  from  springing  line  to  spring- 
ing line  do  press  upon  the  frames,  this 
depending  to  a  very  great  degree  on  the 
curve  of  the  arch.  If,  for  example,  we 
take  the  case  of  a  full  centre  arch  and 
starting  at  the  springing  line  on  either 
side  pass  towards  the  crown,  we  shall 
find  that  for  a  considerable  distance 
above  the  springing  line  the  stones  do 
not  exert  any  pressure  upon  the  ribs, 
but  that,  as  soon  as  this  point  is  passed, 
the  pressure  begins  and  increases  rapidly, 
reaching  its  maximum  intensity  just  be- 
fore the  keystone  course  is  driven  into 
place.  When  this  is  done  the  pressure 


13 

is  almost  entirely  removed,  and  were  it 
not  for  the  slowness  of  the  mortar  in 
drying,  the  frame  work  of  the  arch 
might  be  done  away  with. 

And,  here,  I  would  mention  that,  al- 
though it  is  generally  held  that  when 
the  keying  course  is  placed,  the  vous- 
soirs,  with  the  exception  of  a  few  courses 
at  the  crown,  cease  to  press,  I  have  found 
by  the  most  careful  experiments  with 
large,  well-framed  models,  that  the  thin- 
nest Chinese  paper  when  coated  with 
black  lead  and  placed  under  the  blocks 
of  arch  stone,  could  not  be  drawn  out, 
even  when  the  arch  was  keyed,  without 
considerable  resistance. 

Upon  further  examination  it  will  be 
found  that  these  voussoirs  which  lie  near 
the  springing  line  and  exert  no  pressure 
upon  the  laggings  and  back-pieces,  are 
all  of  them  contained  within  the  angle 
of  repose  ;  that  is  to  say,  the  voussoirs 
do  not  begin  to  press  upon  the  centring 
until  we  reach  one  whose  lower  joint 
makes  so  great  an  angle  with  the  hori- 
zon, that  the  stone  is  caused  to  slide 


14 

along  its  bed  under  the  action  of  gravi- 
tation. This  angle  for  full  centre  arches 
has  been  fixed  at  from  28°  to  30°,  but 
the  quality  of  the  stone  and  mortar  used, 
will  cause  it  to  vary  greatly.  For  ordi- 
nary cut  stone,  we  may  with  safety  as- 
sume the  angle  of  friction  at  30°  with  the 
horizon  :  when  laid  in  thin  tempered 
mortar  it  is  increased  to  34°  or  36°,  and 
with  very  porous  stone,  such  as  free- 
stone, laid  in  full  mortar  it  will  reach 
almost  45°. 

It  is  to  be  observed,  however,  that  this 
is  not  strictly  true  unless  the  arch  is  of 
sufficient  thickness  at  bottom  to  prevent 
all  tendency  to  upset  inwards.  A  thick- 
ness of  TV  the  radius  of  curvature  is  usu- 
ally adopted  as  sufficient  for  this  pur- 
pose. 

Adopting  30°  as  the  angle  of  repose 
for  cut  stone,  the  number  of  voussoirs 
which  load  the  centre  will  depend  on 
the  curve  given  to  the  intrados.  If  we 
take,  for  instance,  a  full  centre,  an  oval 
and  a  flat  segmental  arch,  and  give  to 
each  the  same  number  of  voussoirs,  it  is 


15 

evident  that  the  number  of  stones  which 
do  not  press  on  the  laggings  will  be 
greatest  in  the  full  centre,  less  in  the 
oval,  and  least  of  all  in  the  flat  segmen- 
tal  arch,  because  in  this  latter  case  the 
stone  whose  lower  joint  makes  an  angle 
of  30°  with  the  horizon  will  be  found 
nearer  the  springing  line.  We  should 
expect,  therefore,  the  number  and  weight 
of  the  stones  being  the  same,  that  the 
segmental  arch  could  give  the  greatest 
load  to  the  centres,  and  the  full  centre 
arch  the  least ;  and  this  is  strictly  the 
case. 

In  estimating  the  load  upon  the  centres 
in  any  case,  it  is  to  be  remembered  that 
none  of  the  stones  bear  upon  the  ribs 
with  their  entire  weight,  a  part  of  this 
latter  being  consumed  in  overcoming 
friction.  The  determination  of  the 
amount  of  weight  thus  expended  is  a 
matter  of  some  mathematical  intricacy, 
and  we  are  indebted  for  its  solution  to 
M.  Couplet.*  By  his  calculation  he 

*  M6moire  de  1'Academie  Ann6e,  1792. 


16 

found  that  the  total  weight  of  the  vous- 
soirs  which  do  press  on  the  laggings,  is 
to  the  weight  with  which  they  actually 
load  the  frame,  as  an  arc  of  60°  is  to 
twice  its  sine  less  the  same  angle  ;  or,  to 
express  it  algebraically,  denote  by  P  the 
total  weight  of  the  voussoirs  which  rest 
on  the  centring,  and  by  p,  the  weight 
with  which  they  load  the  centres,  and 
we  shall  have  the  expression 

P  :  p\  iarc  60°  :  2  sin  60°  — arc  60°       (1) 

or 

P  (2  sin  60°  — arc  60°)  .. 

*=  Arc  60.  '      <2> 

If,  therefore,  we  suppose  the  radius  of 
a  circle  to  be  divided  into  10,000  equal 
parts,  the  circumference  will  contain 
62,832,  and  the  arc  of  60°  10,472,  and 
its  sine  is  equal  to  i/\/3,8660.  Substi- 
tuting these  values  in  the  above  equa- 
tion (1),  we  shall  have 

P  :/>::i0472;  ;2X8660— 10472      or 
P  :p\  i  10472  :  6848 

which  gives  us  a  ratio  of  3  to  2  very 


17 

nearly.  Whence  we  see  that  the  vous- 
soirs  in  a  full  centre  arch  which  press 
upon  the  laggings  will  do  so  with  but  f 
of  their  weight,  and,  taking  the  angle 
of  repose  on  each  side  at  30°,  only  on  § 
of  the  surface  of  the  centring.  We 
may,  therefore,  without  any  sensible 
error  take  J  of  the  gross  weight  of  the 
voussoirs  of  the  arch  to  express  the  load 
on  the  centres. 

With  an  arch  which  is  not  full  centre 
the  case  is  quite  similar.  We  will  take 
an  oval  of  three  centres  fulfilling  the 
conditions  that  each  of  the  three  arcs 
composing  it  shall  be  60°.  This  oval 
being  drawn,  it  is  at  once  apparent  that 
the  arcs  of  60°  at  each  end  of  the  oval 
do  not  differ  materially  from  that  of  30° 
in  the  full  centre  arch.  We  may,  there- 
fore, to  facilitate  calculation,  safely  as- 
sume that  the  stones  forming  these  two 
arcs  of  60°  do  not  press  on  the  centres, 
when  the  arch  is  all  up  except  the  key- 
stone, and  are  held  in  place  by  the  weight 
of  the  voussoirs  above  them.  There  re- 
mains then  but  thrrrptrftl  arcf  60°  to 


18 

load  the  framing.  But  from  equation 
(1)  P  :  p  as  the  arc  of  60°  is  to  twice  its 
chord  less  the  arc  of  60°  ;  and  since  60° 
is  to  its  chord  very  nearly  as  22  to  21, 
we  may  without  sensible  error  express 
the  relation  of  P  to  p  by  the  ratio  of  1 1 
to  10.  When  we  have  found  the  gross 
weight  of  the  voussoirs  in  this  arc  of  60° 
it  follows  that  we  must  take  11  of  their 
weight  to  express  the  load  on  the  fram- 
ing. 

The  chord  of  an  arc  of  60°  is  equal  to 
the  radius,  and  the  radius  in  this  case 
being  10000,  the  chord  will  equal  10000, 
and  the  arc  of  60°,  10472.  Hence  we 
have  the  relation  10000  :  10472;  ;21  :  22 
nearly. 

These  values  may  also  be  obtained 
from  the  integral  calculus,  in  which  case 
no  regard  is  taken  of  friction,  and  the 
formulae  are  therefore  a  little  uncertain. 
This  uncertainty,  however,  is  on  the  side 
of  safety,  for  when  we  leave  out  of  con- 
sideration the  pressure  expended  in  over- 
coming friction  we  are  forced  to  give  the 
ribs  and  laggings  unnecessary  strength. 


19 

% 

Referring  to  Figure  1,  we  wish  to  find 
the  load  which  the  voussoirs  between 
A  B  C  D  give  to  the  centre's  rib. 


Let  w  equal  the  weight  per  lineal  foot 
of  intrados  of  the  arch  resting  on 
the  rib. 


20 

r 

By  x  and  y  the  horizontal  and  vertical 

co-ordinates   respectively   of    the 

point  A. 

By  x'  and  y'  the  co-ordinates  of  D. 
By  r  the  radius  of  the  curve  of  intra- 

dos  at  A,  and 
By  x  the  angle  it  makes  with  the  hori- 

zon. 
By  P  the   gross  vertical  pressure  on 

the  rib  of  A  B  C  D. 
By  p  the  pressure  per  lineal  foot  of  in- 

trados  at  A. 

Then  we  shall  have 


From  this  we  may  compute  the  load  on 
any  vertical  post  at  this  point,  or  the 
vertical  component  of  the  load  on  the 
back  pieces. 

If  the  arch  had  been  completed  up  to 
the  keystone  course,  equation  (3)  would 
have  been 


/V 

77 o 


pdx     .     .     .     (4) 


21 

P'  being  the  greatest  vertical  load  on 
the  half  rib,  and  x*  the  horizontal  dis- 
tance from  the  middle  of  the  span  to  a 
point  where  p  is  zero. 

The  value  of  p  is  found  from  the  equa- 
tion 

p= W.  Cos  x  - -1-  /   y  W.  dy     .     (5) 


which  will  evidently  be  greatest  when 
p=W.  Cos  oc  .     .     .     .     (6) 

When  the  arc  is  a  segment  of  a  circle 
not  greater  than  120°,  we  shall  have 
from  the  relation  between  the  sides  and 
angles  of  a  triangle,  the  following  values 
of  the  co-ordinates  : 

x—r  sin  cc  x'=r  sinoc'  x"= r(sin  oc*) 
y— r  (J  —cos  cc  )  y'—r  (1  — cos  oc') 

4 

Substituting  these  values  in  equation  (5) 
we  shall  have 

p—w  (2  cos  oc  —cos  oc').     .     .     (7) 

And  from  the  expression  y=r(l  — cos  X  ) 
we  have 

~  r—  y 

Cos  x  = *  ; 

r 


22 
and  from       y'=r  (1  —  cos  oc') 

Cos  oc'=^' 
r 

Substituting  this  in  equation  (7)  we  shall 
have 


r 
Equation  (6)  then  becomes  p=w  cos  oc 

T  —  I/ 

=w  ----  -  the  greatest  value  for  a  given 

point  of  the  arch. 

Substituting  in  equation  (3)  the  value 
of  p  found  in  eq.  (8),  and,  reducing,  we 
obtain 

(9) 
]*=wr[cc  —  GC'  —  sin  oc  (cos  x  '  —  cos  o>)] 

r 

or 


in  which  I  and  V  represent  the  length  in 
feet  of  the  arcs  from  the  crown  E  (Fig. 
1)  to  the  points  A  and  D  respectively. 
Equation  (4)  then  becomes 


23 

P'=wr  (oc"-sm  <x"  [l  —  cosoc"]  )    (10) 

To  find  the  gross  weight  of  that  por- 
tion of  the  arch  which  presses  on  the 
back  pieces  and  laggings,  it  is  necessary 
to  know  the  number  of  the  voussoirs, 
their  volume  and  weight  per  cubic  foot. 

The  weight  of  stone  generally  used 
in  arches  varies  from  120  to  180  pounds 
per  cubic  foot.  The  following  results 
were  obtained  from  the  examination  of 
a  number  of  -  specimens  of  American 
granite,  sandstone  and  limestone,  taken 
from  the  best  known  quarries  in  the 
country.  Of  seventy-two  specimens  of 
granite  examined,  the  greatest  weight 
per  cubic  foot  was  182.5  Ibs.,  the  least 
161.2,  and  the  average  167.09  Ibs.  Of 
fifty-three  specimens  of  sandstone  exam- 
ined, the  greatest  weight  per  cubic  foot 
was  164.4  Ibs,  the  least  127.5,  and  the 
average  140.9  Ibs.  Of  thirty -eight 
sr'e~::::  :ns  of  limestone,  the  greatest 
weight  per  cubic  foot  was  173.8,  the  least 
143.2,  the  average  162.9. 
We  may  therefore  without  sensible 


24 


error  assume  the  average  weight  of  these 
three  classes  of  stone  as  follows  : 

Average  weight 
per  cubic  foot . 

Granite 167.09  Ibs. 

Sandstone 140.9    Ibs. 

Limestone 162.9    Ibs. 

Brick  (well  burnt) 92.0    Ibs. 

From  the  moment  the  angle  of  repose 
is  passed  and  the  first  voussoir  begins  to 
press  on  the  frames,  the  centring  be- 
comes subjected  to  a  series  of  strains 
which  increase  rapidly  up  to  the  time 
the  keystone  is  laid,  and  are  produced 
by  the  yielding  of  the  ribs  under  the 
weight  of  the  stones.  No  matter  how 
well  seasoned  and  admirably  proportion- 
ed the  timbers  may  be,  or  how  evenly 
the  load  may  be  distributed,  the  centre, 
pressed  more  and  more  severely  on  each 
side  by  the  successive  courses  of  vous- 
soirs  laid  upon  it,  will  bend  in  on  the 
sides,  and  as  a  consequence  bulge  out  at 
the  crown,  to  be  in  turn  followed  by  a 
bending  in  of  the  crown  when  the  arch 
is  all  but  completed.  This  movement  of 


25 

the  ribs  can  be  greatly  checked  and  the 
severity  of  the  resulting  strains  much 
lessened  by  loading  the  centres  at  the 
crown  with  the  spare  voussoirs  and  in- 
creasing the  load  as  the  arch  progresses. 
In  the  case  of  a  full  centre  arch  of  90 
feet,  and  composed  of  four  hundred  and 
eighty  courses  of  voussoirs,  the  cen- 
tring, when  the  fifteenth  course  of  vous- 
soirs on  each  side  were  laid  in  place,  had 
risen  three  inches  at  the  crown.  When 
loaded  with  325,000  Ibs.,  it  settled  under 
it  two  inches  ;  but  when  the  twentieth 
course  was  completed  the  pressure  was 
so  great  that  it  again  rose  one  inch. 
When  the  arch  was  three-quarters  com- 
pleted it  had  again  sunk  one  inch  and 
three-quarters  in  consequence  of  the  ad- 
ditional load  and  the  compression  of  the 
wood,  still  leaving  a  rise  of  one  quarter 
of  an  inch.  This  yield  caused  the 
joints  at  the  twenty-second  course  to 
open  a  fraction  of  an  inch,  but  closed 
when  the  keystones  were  driven.  This 
distortion  of  the  centring  is  always 
greatest  for  full  centre  arches,  and  pro- 


26 


portionally   less    as    the    arch   becomes 
nearer  and  nearer  to  the  segmental. 

DIRECTION    OF    THE    STRAINS. 

To  find  the  direction  and  intensity  of 
the  strain  at  any  point  of  the  rib,  we  re- 
sort to  the  usual  method  of  the  "  paral- 
lelogram of  forces."  Returning  to  Fig. 
1,  let  it.be  required  to  find  the  direction 
of  the  strain  caused  by  the  voussoirs 
A  B  C  D.  Denote  by  F  the  centre  of 
gravity  of  this  part  of  the  arch,  and 
through  it  draw  a  vertical  line  G I  of  in- 
definite length,  and  cut  it  at  I  by  a  per- 
pendicular from  the  point  E  at  which 
the  curve  drawn  through  the  centres  of 
gravity  of  the  voussoirs — supposed  in- 
definitely small — cuts  the  line  AB. 
Complete  the  parallelogram  by  drawing 
;  the  line  IM  to  the  centre  of  arch,  and 
NL  parallel  to  it.  The  diagonal  IN 
will  then  express  the  weight  of  the  vous- 
soirs A  B  C  D,  the  side  I L  the  pressure 
they  exert  upon  the  lower  part  of  the 
arch,  and  the  side  I M  the  pressure  upon 
the  backpieces  o  the  rib. 


The  strains,  then,  upon  the  centring 
take  the  direction  of  the  radius  of  cur- 
vature of  the  intrados,  and  it  now  re- 
mains to  consider  the  position  which 
should  be  given  to  the  beams  which  are 
to  withstand  the  strains,  their  number 
and  dimensions. 

THE    PRINCIPAL   BEAMS    AND   THEIR 
POSITION. 

As  the  sole  object  of  the  framing  is  to 
uphold  the  voussoirs  and  transmit  the 
strains  it  receives  as  directly  as  possible 
to  firm  points  of  support,  the  beams  must 
be  so  arranged  as  to  do  this  with  the 
least  tendency  to  change  the  shape  of 
the  rib,  by  their  bending  or  breaking. 
The  condition  will  be  best  fulfilled  by 
giving  each  beam  a  position  such  that  it 
shall  offer  the  greatest  possible  resist- 
ance, and  this  will  be  accomplished  when 
the  direction  of  the  fibres  of  the  beam 
and  the  direction  of  the  strain  are  one 
and  the  same. 

If,  for  instance,  we  support  a  horizon- 
tal beam  at  its  two  ends  and  load  it  in 


28 

the  middle  it  will  offer  its  least  resist- 
ance to  the  load.  If  now  we  raise  one 
end  so  that  the  direction  of  the  strain  is 
oblique  to  the  fibres  of  the  beam,  the  re- 
sistance of  the  beam  to  bending  will  be 
found  to  have  increased  largely,  and  the 
resistance  in  this  latter  case,  will  be  to 
that  in  the  former  case,  as  the  cosine  of 
the  angle  made  by  the  direction  of  the 
strain  and  the  fibres  of  the  wood  is  to 
the  sine  of  90°  or  1. 

It  should  follow  from  this  that,  when 
the  angle  between  the  beam  and  the 
strain  is  zero,  the  resistance  becomes  in- 
finite, and  such  would  indeed  be  the  case 
were  it  not  for  the  compressibility  of  the 
wood  and  other  physical  causes  which 
weakens  its  strength.  It  is  sufficient, 
however,  for  us  to  know  that  when  the 
strain  is  carried  through  the  axis  of  the 
beam,  it  is  then  strongest,  and  that  as 
the  force  becomes  more  and  more  oblique 
to  the  fibres  its  strength  decreases. 

Applying  this  fact  to  the  framing  of 
the  ribs,  it  follows  that  the  greatest  stiff- 
ness and  strength  will  be  gained  when 


29 

the  principal  pieces  are  placed  in  the 
direction  of  the  strains,  or  in  the  direc- 
tion of  the  radii  of  curvature  of  the 
arch  to  be  upheld.  This  deduction,  un- 
fortunately, is  under  certain  restrictions 
placed  upon  it  by  the  imperfections  of 
the  timber,  and  demands  of  economy 
and  the  circumstances  of  construction, 
which  make  its  practical  application  quite 
limited. 

To  illustrate,  we  will  once  more  return 
to  Fig.  1.  The  direction  and  intensity 
of  the  strain  on  the  backpieces  resulting 
from  the  weight  of  the  voussoirs  ABCD, 
will  then  be  represented,  as  we  have 
just  seen  by  the  line  V  M,  and  that  of 
the  voussoirs  P  Q  by  the  line  V  S.  The 
beams,  therefore,  which  are  to  support 
these  stones,  in  order  that  they  may  of- 
fer the  utmost  resistance,  must  take  the 
direction  of  the  lines  V  S  and  V  M,  or 
radiate  from  the  centre  V  like  the  spokes 
of  a  wheel.  For  small  span  arches,  such 
an  arrangement  of  beams  undoubtedly 
answers  all  purposes  of  stiffness  and 
economy,  but  for  arches  of  larger  span 


30 

where  timbers  of  thirty,  fifty,  or  even  a 
hundred  feet  in  length  would  be  requir- 
ed, it  fails  most  signally  ;  for  while  a 
beam  of  ten  feet  will  offer  great  resist- 
ance to  compression  when  loaded  in  the 
direction  of  the  fibres,  a  beam  of  fifty 
feet  will  be  almost  sure  to  bend  under 
the  action  of  the  strain,  and  hence  re- 
quire bracing.  This  system,  therefore, 
cannot  be  successfully  carried  into  prac- 
tice in  large  span  centres. 

To  overcome  this  difficulty  we  are 
forced  to  resolve  the  force  represented 
by  the  line  S  Y  into  two  components,  one 
vertical  and  represented  by  the  line  S  T, 
and  one  horizontal  represented  in  direc- 
tion and  intensity  by  S  R.  By  a  similar 
treatment  of  the  force  represented  by 
V  M,  we  shall  obtain  two  other  similar 
lines,  all  four  of  which  will  represent  the 
direction  of  three  beams,  which  can  be 
made  to  take  the  direction  of  the  two 
V  S  and  V  M,  namely,  a  long  horizontal 
beam  spanning  the  arch  and  supported 
at  each  end  by  a  vertical  beam.  This 
horizontal  beam  is  the  tie  beam  to  which 


31 

we  have  already  alluded,  and  is  gener- 
ally placed  at  points  about  45°  up  the 
arch.  The  voussoirs  above  this  beam 
are  then  supported  by  another  horizon- 
tal tie  upheld  by  small  vertical  beams 
abutting  on  the  lower  tie.  An  excellent 
illustration  of  this  system  of  framing  is 
found  in  centres  of  London  Bridge  over 
the  Thames,  built  in  1831  by  Rennie. 

There  will  frequently  arise  cases  in 
which  ribs  framed  in  this  manner  either 
on  account  of  the  quantity  of  material 
they  consume,  or  the  difficulty  of  finding 
firm  points  of  support  between  the  abut- 
ments, cannot  be  used  to  advantage.  It 
then  becomes  necessary  to  change  the 
point  of  support  T  of  the  beam  ST 
(Fig.  1)  to  a  point  t  nearer  the  abutment, 
and  for  the  sake  of  economy  we  may  do 
away  with  the  horizontal  and  vertical 
beams  tg,  s  S,  T  S,  c  a  and  a  b,  supply- 
ing their  place  by  two  beams  t  S  and  S  e. 
These  two  beams,  therefore,  will  sustain 
the  strain  represented  by  the  line  S  V, 
and  the  efforts  they  resist  will  be  repre- 
sented in  direction  and  intensity  by  the 


32 

sides  S  X  and  S  Y  of  the  parallelogram 
XY  constructed  on  S  V  as  a  diagonal. 

In  "cocket"  centres,  therefore,  what- 
ever the  span  of  the  arch,  whether  large 
or  small,  whatever  the  shape,  whether 
full  centre,  oval  or  segmental,  a  great 
saving  of  material  may  be  made,  and 
abundance  of  strength  may  be  secured, 
by  placing  the  principal  beams  in  the 
direction  of  the  chords  of  the  curve  of 
the  intrados. 

The  length  that  should  be  given  to 
beams  thus  placed,  the  angle  they  should 
make  with  each  other  at  their  point  of 
junction,  the  manner  of  supporting,  and 
when  necessary  bracing  them,  are  points 
we  shall  reserve  for  future  consideration. 

There  are,  therefore,  three  methods  of 
arranging  the  principal  pieces  or  struts 
of  a  centre  frame. 

1°.  They  may  be  placed  in  the  direc- 
tion of  the  radii  of  curvature  of  the 
arch,  thus  giving  a  figure  of  invariable 
form  as  the  strain  at  any  one  point  is  re- 
ceived by  the  beam  in  the  most  favor- 
able position,  and  transmitted  through 


33 

its  axis  directly  to  the  fixed  point  of  sup- 
port. 

2°.  They  may  be  placed  in  a  vertical, 
or  in  vertical  and  horizontal  directions. 

3°.  The  curve  of  the  arch  may  be  di- 
vided into  a  number  of  arcs,  and  the 
beams  placed  in  the  direction  of  the 
chords  of  these  arcs. 

4°.  To  these  three  we  may  add  a  fourth, 
which  embraces  by  far  the  largest  num- 
ber of  centre  frames,  and  is  based  on 
two  or  all  of  the  preceding  methods.  In 
this  class  the  beams  are  not  arranged  in 
accordance  with  any  one  system,  but 
several ;  as,  for  instance,  the  second  and 
third,  in  which  case,  as  we  shall  see  here- 
after, several  straining  beams  span  the 
arch  at  different  points,  and  are  sustain- 
ed by  inclined  struts  ;  or  if  all  three  sys- 
tems are  used,  we  may  use  the  straining 
beam  and  inclined  struts,  and  strengthen 
them  by  bridle  pieces  in  the  direction  of 
the  radii. 

It  would,  indeed,  be  quite  a  hopeless 
task  to  attempt  to  lay  down,  in  more 
than  a  general  way,  the  principles  which 


34 

ought  to  rule  in  making  a  selection  of 
one  of  these  methods  to  the  exclusion  of 
the  remaining  three.  In  every  case  the 
choice  must  be  determined  largely  by  the 
circumstances  of  the  case,  the  points  of 
support,  the  shape  and  span  of  the 
frame,  and  the  strength  required.  If  the 
centre  is  to  be  "  cocket,"  the  arch  heavy, 
the  span  large,  and  considerable  head- 
way required  beneath  the  frame,  the 
third  or  fourth  arrangement  will  undoubt- 
edly afford  the  best  results  whatever 
may  be  the  shape  of  the  arch.  If  the 
arch  is  light,  the  span  moderate,  and  little 
or  no  headway  is  wanted,  then  the  sec- 
ond or  first  will  generally  be  most  con- 
venient. 

Theoretically,  the  first  method  will  in 
all  cases  afford  the  greatest  amount  of 
strength  and  stability  with  the  least 
amount  of  material,  since  the  beams  are 
then  capable  of  resisting  the  most  se- 
vere strains.  Nor  can  there  be  any 
doubt  that,  within  moderate  limits,  this 
result  actually  is  attained  in  practice, 
and  that  of  two  ribs  constructed  with 


35 

the  same  number  of  beams,  of  the  same 
quality  of  wood  and  similar  dimensions, 
in  one  of  which  the  pieces  are  placed 
radially,  and  in  the  other  vertically  or 
inclined,  the  rib  arranged  on  the  former 
plan  will  be  decidedly  the  stronger  of 
the  two.  But,  unfortunately,  the  im- 
possibility of  always  obtaining  firm 
points  of  support  at  the  centre  of  curva- 
ture, the  difficulty  of  finding  sound,  well 
seasoned  timber  of  such  length  as  would 
be  required  in  arches  of  large  span,  and 
the  relation  which  exists  between  the 
length  and  strength  of  beams  under 
longitudinal  compression — the  strength 
varying  inversely  as  the  square  of  the 
length — restricts  its  application  to  cen- 
tre frames  of  very  small  span  and  rise. 
In  semi-circular  arches  of  twelve,  fifteen 
or  even  twenty  feet  span,  when  a  hori- 
zontal beam  can  be  used  at  the  springing 
line  this  arrangement  can  be  used  with 
great  success.  The  frame  then  consists  of 
the  tie  beam  and  two,  or  if  great  strength 
is  required,  three  radial  struts  which  sup- 
port the  backpieces  and  abut  against  the 


36 

horizontal  beam  at  the  centre  of  curva- 
ture. These  struts,  when  two  are  used, 
should  be  inclined  on  the  right  and  left 
at  a  little  less  than  45°  to  the  horizon,  so 
as  to  meet  the  backpieces  at  the  point 
where  the  voussoirs  first  begin  to  press 
on  the  rib.  A  vertical  strut  is  in  such 
an  arrangement  of  little  or  no  use,  as  no 
strain  of  any  consequence  can  possibly 
reach  it  ;  the  voussoirs  almost  ceasing  to 
press  on  the  frame  when  the  keystone 
is  driven  down.  As  these  supports  are 
struts  and  not  bridle  pieces  clamping  the 
backpieces  and  tie  beam  between  them, 
the  joints,  especially  in  the  larger  and 
heavier  arches,  must  be  secured  by  pieces 
of  iron  placed  across  them  and  bolted  to 
the  backpieces  and  struts,  to  prevent  the 
joints  opening  in  consequence  of  the 
bulging  at  the  crown  as  course  after 
course  of  stone  is  laid  on  the  frame. 

In  frames  for  flat  segmental  arches  of 
a  span  as  great  as  sixty  or  seventy  feet 
and  rise  of  about  one-fifth  the  span,  as 
also  for  ovals  of  several  centres,  this 
radial  arrangement  may  be  slightly  modi- 


38 

fied  and  a  frame  produced  (Figure  2), 
which  shall  meet  all  the  requirements  of 
strength,  lightness  and  economy.  The 
rib  in  this  case  again  consists  of  a  hori- 
zontal tie  beam  spanning  the  arch  a  little 
above  the  springing  line,  generally  at 
the  first  voussoir  that  presses  on  the 
backpieces,  and  struts  placed  in  the  di- 
rection of  the  radii  of  curvature  and 
from  eight  to  ten  feet  apart  depending 
on  the  weight  of  the  arch.  These  struts, 
as  it  would  be  impossible  to  have  them 
actually  meet  at  the  centre  of  curvature, 
which,  for  an  arch  of  seventy  feet  span 
and  fifteen  feet  rise,  would  be  about 
forty-five  feet  from  the  circumference, 
go  no  further  than  the  tie  beam  and  are 
fastened  to  it  and  the  backpieces  by  the 
iron  bands  shown  in  the  figure. 

When  great  stiffness  is  required  in  the 
rib,  additional  braces  may  be  added,  as 
shown  in  Fig.  2,  dividing  the  rib  into  a 
number  of  triangles.  The  strains  re- 
ceived will  then  be  transmitted  through 
the  axes  of  the  beams,  and  as  all  unnec- 
essary transversal  strains  will  be  avoid- 


39 

ed,  the  resistance  offered  by  the  braces 
will  be  the  greatest  possible.  In  all 
centre  ribs,  the  normal  pressure  being 
in  the  direction  of  the  radii  of  curvature, 
the  laggings,  backpieces  and  tie  beam, 
when  used,  will  of  necessity  be  subject- 
ed to  transversal  strain. 

Before,  however,  we  proceed  to  con- 
sider the  strains  to  which  the  beams  in 
centre  frames  are  subjected,  and  the  di- 
mensions we  must  give  them  in  order 
that  they  may  withstand  the  pressure 
put  upon  them,  we  would  offer  the  fol- 
lowing practical  rule  for  estimating  the 
pressure  of  any  arch  stone  in  any  part 
of  the  arch,  upon  the  centre  rib,  or  the 
pressure  upon  the  rib  at  any  stage  of  the 
construction  of  the  arch,  as  also  the 
pressure  when  the  arch  is  completed  up 
to  the  key  stone. 

It  has  been  well  established  by  the  ex- 
periments of  Rondelet,  that  a  stone 
placed  upon  any  inclined  plane  does  not 
begin  to  slide  on  that  plane  until  it  has 
reached  an  angle  of  inclination  to  the 
horizon  equal  to  30°.  It  is  obvious, 


40 

therefore,  that  if  the  arch  stones  were 
placed  upon  one  another  they  would  not 
begin  to  press  on  the  centre  rib  till  the 
plane  of  the  lower  joint  of  one  of  them 
reached  an  angle  of  30°  with  the  horizon. 
It  has  been  found,  moreover,  that  the 
mortar  increases  this  angle,  for  hard 
stone  to  34°  or  36°,  and  for  soft,  porous 
stone  (in  semi-circular  arches)  to  42°. 
We  may,  then,  consider  the  pressure  to 
commence  in  general  at  the  joint  which 
makes  an  angle  of  32°  with  the  horizon. 
If  we  suppose  the  radius  to  represent 
the  pressure  the  tangent  will  then  repre- 
sent the  friction,  and  making  the  radius 
unity  the  friction  will  be  0.625.  The 
next  stone  will  press  a  little  more,  the 
third  still  more,  and  the  pressure  will 
thus  continue  to  grow  larger  and  larger 
with  each  succeeding  course.  The  rela- 
tion between  the  weight  of  an  arch  stone 
and  its  pressure  upon  the  rib  in  the  di- 
rection perpendicular  to  the  curve  is 
given  by  equation  : 

Q— W  (cos  a- /sin  a)      .     .     (11) 
in  which  Q  is  the  pressure,  W  the  weight 


41 

of  the  arch  stone,/* the  friction  =:  0.625, 
and  a  the  angle  the  lower  joint  makes 
with  the  vertical.  The  following  table 
calculated  from  eq.  11,  gives  the  value 
of  Q  for  every  2°  of  curve  from  the 
angle  of  repose  =  32°  up  to  60°  : 

When  the   angle  which  the  joint  makes 

with  the  horizon  is 

34° then  Q=.04  W 

When   36° "  Q  =  .08  W 

"      38° "  Q=.12W 

"      40° "  Q  =  .17W 

"       42° "  Q=.21  W 

"       44°.....     "  Q=.25W 

"      46° "  Q=.29W 

"       48° "  Q  =  .33W 

.  "      50° "  Q  =  .37  W 

«       52° "  Q=.40W 

"       54° "  Q=.44W 

"       56° "  Q=.48W 

"       58° "  Q=.52W 

"       60° "  Q  =  .54W 

To  take  an  example  :  What  is  the 
pressure  on  a  backpiece  of  20°  in  length 
from  the  angle  of  repose,  the  ribs  of  the 


42 


frame  being  placed  5  ft.  from  centre  to 
centre,  and  the  arch  stones  3  ft.  in  depth 
and  weighing  160  Ibs.  per  cubic  foot. 
We  take  from  the  above  table  the  sum 
of  the  decimals  from  32°  —  52°=  2.26,  and 
multiply  this  by  the  weight  upon  2°  and 
the  product  will  equal  the  pressure. 
The  volume  of  the  stones  which  cover 


The  number  of  feet  contained  in  2°  is 
found  from  the  expression  2  X.  01  745  329 
Xr',  in  which  r'  is  equal  to  the  radius 
of  the  arch  plus  one  half  the  depth  of  the 
arch  st,one.  If  we  take  the  radius  =  25 
ft.,  then  the  depth  of  the  stones  being  3 
ft,  r'  =  26.5  and  number  of  feet  in  2° 
equals  .88  ft.,  whence  the  volume  of  the 
stones  which  press  on  the  2°  equals 
5X3X.88  =  13.4  cubic  feet,  and  the 
quantity  W=2144  Ibs.  and  Q,  or  the 
pressure  on  the  backpiece  equals  4845 
Ibs. 

If  we  denote  by  a  the  angle  included 
between  the  upper  and  lower  joints  of 
an  arch  stone,  and  suppose  every  stone 
in  the  arch  to  have  the  same  weight  and 


43 


equal  angle  a,  then  the  pressure  of  any 
number  n  of  such  stone  upon  the  rib  will 
be  given  from  the  expression 

n+I  (12) 

W  +  sin  -  a.  ,  , 
Q=  2      X(cos 


sin  J  a 

which  gives  the  total  pressure  on   one 
half  of  the  rib. 

This  equation  is  found  as  follows  : 
The  pressure  perpendicular  to  the  soffit 
is  W  (sin  a—  f  cos  a),  or  W  (cos  a—f 
sin  a),  according  as  the  angle  a  is  mea- 
sured from  the  horizon  or  from  the  ver- 
tical drawn  through  the  crown.  If  now 
we  denote  by  a  the  angle  included  be- 
tween the  joints  of  one  stone,  and  sup- 
pose each  stone  alike  in  size  and  weight, 
the  pressure  of  any  number  n  of  such 
stones  will  evidently  be  found  by  getting 
the  sum  of  the  sines  and  cosines  of  n  a, 
or  expressed  in  formula, 

Pz=W  (sum  of  cosines  of  na—  /xsum 
of  sines  of  na)     .     ,     ;     .     Eq.  A. 

By  trigonometry  we  obtain  two  expres- 
sions for  the  sum  of  the  sines  and  cosines 


44 

of  a  number  of   angles  in  arithmetical 
progression,  viz.  : 

Sin  A  +  sin  (A  +  B)-fsin  (A  +  ^B) 
__Cos  (A—  JB)  —  cos  (A-f  rc  +  £B) 

2  sin  i  B 
Sin    A  +  j^BXsin       M  +  !    B 


sin  -g  B. 
Also 

Cos  Af  cos  (A  +  B)  +  cos  (A  +  wB) 

—  cos    A  +  |^BXsin  £  (w+1    B 


sin  -J  B. 

Applying  these  two  equations  to  the 
above  case,  we  shall  have  from  eq.  A, 

P=W  Eq.  B. 

n  n+1        -,  .    n         .    n  +  I 

cos  -  a  X  sin  -  a—  /(sin  -  aX  sin  —  —  —  a) 

22  22 

sin  £  a. 
Or  taking  out  the  common  factors  W  and 

K+l 

sin     2        we  shall  have  equation  B  in 

sin^  a 
the  form.  Eq.  (12) 

^     WXsin  ^—  —     x/        w  .    n 

P=±  2    aXlcos  p  a~c/  sm  ~a 

sin  -J  a 


45 

The  value  of  Q  may  also  be  obtained 
from  eq.  11  by  considering  that  when 
the  depth  of  the  arch  stone  is  nearly 
double  its  thickness  ;  its  weight  rests  on 
the  rib  at  the  angle  of  60°.  Equation  12 
is,  however,  the  best,  and  may  be  readily 
solved  by  logarithms. 

For  example  :  let  the  arch  be  semi- 
circular and  a—2°y  then  na=29°  and 
f=.625.  Put  equation  12  in  the  form 

COS 


>...'  "i  .     w  +  1 

/  sm  ^  /I  aXsm          a 

_____________^_____     

sin  £  a  x  R 

log  cos   na  =log  cos  29°  =  9.941819 

,    w-f  1 
log  sm  ——a— log  sm  30  =9.698970 


19.639789 


log  sin  |  a  =  log  sin  1°=   8.241855 
R          =10.000000 


18.241855 


46 

Difference—   1.397934 
=  log  24.68 

log/   =    log  .625=  --    1.795880 
log  sin£  na=^\og  sin  29°  =  9.685571 

n-\- 1 
log  sin a— log  sin  30°=9.698970 


19.180421 

log  sin  ^  a  =  log  sin  1°=   8.241855 
R  =10 


18.241855 

Difference^  0.938669  = 
log  8.55 

Hence   the  weight   on  the  half    rib   is 
24.68  —  8.55  =  16.13  W. 

In  a  frame  constructed,  as  that  shown 
in  Fig.  2,  the  determination  of  the 
strains  is  a  matter  of  great  simplicity, 
and  may  be  had  either  from  arithmetical 
calculation  or  by  constructing  the  paral- 
lelogram of  forces.  The  strain  on  any 
radial  strut  as  B  G  would  be  found  by 
calculating  from  eq.  11  the  pressure  on 
D  E,  taking  half  of  it  and  supposing  it  to 


47 

act  at  B  in  the  direction  B  G.  The  strain 
on  any  inclined  strut,  as  E  G  or  E  H,  may 
be  found  by  estimating  from  eq.  11,  the 
strain  on  B  H  taking  one  half  of  it,  and 
supposing  it  to  act  at  E  in  the  direction 
of  the  radius  at  that  point,  and  denote 
by  b  and  b'  the  angles  these  pieces  make 
with  the  direction  of  the  force.  Then, 
if  these  angles  are  unequal 

8=    P;ln  S'       and  S'=J^*v  (13) 

sm  (b  +  b')  sin  (b  +  b')  v 

And  if  the  two  beams  make  equal  angles 
with  the  direction  of  the  force,  then  the 
strain  in  the  direction  of  each  is  the  same 
and  expressed  by 


Of  all  methods  of  calculating  the  strain 
on  the  different  beams,  by  far  the  sim- 
plest, is  to  actually  construct  the  dia- 
gram of  forces  to  a  given  scale  and  find 
the  pressure  by  measurement.  In  above 
case,  for  example,  draw  E  e  parallel  to 
the  direction  of  the  force  to  any  con- 


faHIVEESITT) 


48 

venient  scale,  say  i1*  inch  equal  1,000 
Ibs.,  which,  supposing  the  pressure  at 
E=10,000  Ibs.  will  make  Ee=one  inch. 
From  E  draw  E#  parallel  to  E  G;  'also 
E  h  parallel  to  EH,  and  eg  to  EA  and 
eh  to  E#.  Then  E#  being  measured 
will  give  the  pressure  on  the  beam  E  G 
to  which  it  is  drawn  parallel. 

When  we  have  once  ascertained  the 
strain  which  any  beam  in  a  frame  will 
have  to  undergo  and  resist,  the  next  step 
is  to  determine  the  dimensions,  or  rather 
the  area  of  cross  section,  the  beam  must 
have  to  withstand  this  pressure  without 
injury.  Whatever  may  be  the  length  of 
the  beam,  this  section  may  be  obtained 
from  the  following  formulae  :  If  the 
strain  is  one  of  compression  in  the  direc- 
tion of  the  length,  then 


in  which  A  is  the  section  required  in 
square  inches,  F  the  crushing  force  to 
which  the  beam  is  subjected,  and  K  the 
resistance  to  crushing.  When  the  strain 
is  a  transverse  or  breaking  strain,  then 


49 


in  which  K'  is  the  modulus  of  rupture  of 
the  beam. 

In  place  of  K  and  K',  however,  which 
are  the  ultimate  resistance  to  crushing 

K  K' 

or  rupture,  we  must  use  —  and  — ,  in 

n  n 

which  n  is  the  factor  of  safety,  usually 
taken  as  10  for  wood.  The  values  of  K 
and  K'  are  variously  stated  by  different 
writers  on  the  strength  of  materials. 
Those  given  below  for  the  woods  mostly 
used  in  centre  frames  are  from  Rankine: 


Wood. 

Value  of 
K  in  Ibs 

Value  of  K' 
in  Ibs. 

Ash      

9,000 

12,000 

Pine  yellow  

5,400 

9,900 

Pine,  red  

6,200 

7,100 

Oak  English  

10,000 

10,000—13,000 

Oak,  American  

6,000 

10,600 

If  it  is  not  always  possible  to  obtain 
these  values  of  K  and  K',  a  very  safe 
method,  and  one  easily  remembered,  i& 


50 

to  find  from  the  diagram  of  forces  the 
strain  on  a  beam  in  Ibs.,  and  divide  this  by 
1,000;  the  result  will  be  the  cross  section 
of  the  beam  in  inches.  Thus,  if  a  tim- 
ber is  loaded  with  36,000  Ibs.,  '  —36 
in.,  and  the  beam  should  be  6  in.X6  in. 

Example. 

Required  the  proper  dimension  of 
the  scantling  of  a  centre  rib  of  a  seg- 
mental  arch  of  60  feet  span  and  9  feet 
rise  ;'  the  arch  stones  to  consist  of  old 
quarry  granite,  weighing  165  pounds  per 
cubic  foot,  and  three  feet  in  depth  ;  the 
rib  to  be  of  the  pattern  shown  in  Fig.  2. 
The  frames  to  be  placed  5  ft.  from  centre 
to  centre. 

The  first  step  is  to  find  the 
weight  of  the  arch  stone  for  1°  of  the 
curve.  The  span  is  60  ft.,  the  radius  is 
50  ft.,  and  the  arch  stones  being  3  ft. 
thick  the  radius  of  the  arch  passing 
through  their  centre  is  51.5  ft.  The 
length  of  1°  is,  therefore,  .01745329X 
-51.5  =.89  ft.  Then  5X3X-89  =  13.3 


51 

cubic  ft.,  the  solid  contents  of  1°  of  the 
arch  ring,  and  this  multiplied  by  165 
gives  the  weight  of  1°=  13.3X165  = 
2195  pounds.  Now  the  arch  being  a 
very  flat  segmental,  it  is  evident  that  all 
the  arch  stones  will  press  upon  the  rib. 
If  then  we  calculate  the  weight  of  the 
stones  between  E  E',  and  suppose  them 
to  act  with  one  half  their  entire  weight 
at  C  in  the  direction  CH,  it  is  evident 
that  this  will  be  the  greatest  pressure 
that  C  H  will  be  required  to  support. 
The  arc  EE'=:200,  and  the  weight  for 
1°  being  2195  Ibs.,  the  pressure  at  C  i» 
21950  Ibs.,  and  the  beam  CH  should  be 

21950 

=  21.9  inches  or4^X^  in.     To  find 


the  dimensions  of  E  G  and  E  H  take  eq. 
12.  Then  a=l°,  w=20°,  /=.625,  W 
=  2195. 


173648)  =  18301  Ibs. 

Take  this  and  lay  it  off  to  any  conven- 
ient scale  on  the  line  E  0,  and  from  E 


52 

draw  EC/  parallel  to  EG,  and  EA  to 
EH  and  as  before  eg  and  eh.  Then 
measuring  E  h  by  the  same  scale  it  will 
be  found  to  equal  10250  Ibs.  ;  the  beam 
EH  then  must  be  3j  in.  by  3  in.  In  the 
same  manner  the  pressure  on  B  G  is  found 
to  be  18301  Ibs.,  and  the  beam  must  be 
4£  in.X4  in.  To  find  the  strain  on  the 
inclined  strut,  estimate  from  eq.  12  the 
weight  of  the  arch  stones  between  A 
and  C,  add  to  this  half  the  weight  of 
the  rib  and  let  the  gross  weight  act  ver- 
tically at  the  point  K,  and  lay  it  off  to 
any  scale  on  the  vertical  line  KK',  and 
draw  K'  I/  parallel  to  the  horizontal  tie 
beam.  The  line  K  L'  being  measured 
will  give  the  strain  on  the  beam  K  L'. 

Frames  arranged  on  the  second  meth- 
od, with  the  principal  pieces  all  vertical, 
afford  centres  of  great  simplicity  of 
structure  and  of  almost  as  much  strength 
as  one  with  radial  struts — supposing,  of 
course,  that  the  number  and  dimensions 
of  the  struts  are  the  same  in  each  case — 
and  of  much  greater  strength  than  one 
constructed  with  inclined  beams,  since 


53 

the  nearer  the  aiigle  the  direction  of  the 
strain  makes  with  the  fibres  of  the  wood 
approaches  a  right  angle  the  less  be- 
comes the  resistance  of  the  beam.  In 
segmental  and  oval  arches  of  large  span, 
the  difference  in  the  strength  of  ribs  ar- 
ranged on  the  vertical  and  radial  plan 
is  comparatively  insignificant,  as  the 
radius  being  very  large,  the  vertical 
beams,  especially  near  the  crown  where 
the  strain  is  severe  and  most  strength 
is  required,  do  not  depart  much  from  the 
direction  of  the  radius. 

The  objection  to  this  vertical  bracing 
of  the  frame  is  that  it  requires  the  use 
of  a  horizontal  tie  beam,  unless  the  rib 
is  constructed  as  a  girder  resting  upon 
framed  abutments  of  its  own.  If  the 
former  arrangement  is  used,  the  struts 
should  be  placed  from  five  to  eight  feet 
apart,  depending  on  the  strength  requir- 
ed, and  mortised  to  the  tie  beam  and 
backpiece.  When  the  beams  are  of  such 
length  that  there  is  danger  of  their  bulg- 
ing or  curving  under  the  load  laid  on 
them,  they  may  be  strengthened  by  di- 


54 

agonal  braces  or  horizontal  wales.  Of 
the  two,  the  diagonal  braces  are  to  be 
preferred  as  they  not  only  give  stiffness 
to  the  posts,  but  sustain  a  portion  of  the 
load  on  the  backpieces  in  case  any  of  the 
piles  under  the  horizontal  tie  beam  should 
give  way.  Figure  3  represents  the  rib 
of  a  full  centre  arch  of  75  ft.  span  ar- 
ranged with  the  principal  pieces  placed 
vertically  and  strengthened  with  a  hori- 
zontal waling  piece  made  double,  and 
braces  abutting  under  the  backpieces. 
The  strains  on  the  different  beams  com- 
posing such  a  frame,  and  their  necessary 
dimensions  may  be  computed  with  ease 
by  the  method  just  explained.  It  should, 
however,  be  remembered  that  beams 
which  are  to  be  notched  must  have  their 
dimensions  increased  beyond  those  given 
by  calculation,  in  as  much  as  notching 
will,  even  when  not  very  deep,  cut  down 
the  strength  of  a  beam  from  one  third 
to  one  half.  In  computing  the  strains 
on  the  braces  a,  a,  we  may  consider  the 
pressure  at  their  abutting  point  to  be 
the  sum  of  the  pressures  on  the  vertical 


55 


56 

and  two  inclined  braces  which  meet 
there,  and  make  no  allowance  for  the 
resistance  of  the  horizontal  beam. 

The  third  and  fourth  systems  of  ar- 
ranging the  principal  pieces,  afford  an 
almost  unlimited  number  of  designs  for 
centre  ribs,  which  are  especially  worthy 
of  notice,  in  that  they  are  applicable  to 
every  possible  shape  and  span  that  can 
be  given  to  stone  arches,  and  may  be 
constructed  with  or  without  intermediate 
points  of  support,  according  as  circum- 
stances will  admit.  The  principles  which 
control  such  arrangements  are  few  and 
simple.  'The  beams  should  as  far  as  pos- 
sible abut  end  to  end:  they  should  inter- 
sect each  other  as  little  as  may  be  since 
every  joint  causes  some  degree  of  set- 
tlement, and  halving  destroys  fully  half 
the  strength  of  the  beams  halved. 
When  the  framing  is  composed  of  a 
number  of  beams  crossing  each  other, 
pieces  tending  towards  the  centre  should 
be  notched  upon  and  bolted  to  the  fram- 
ing in  pairs  :  ties  should  also  be  continu- 
ed across  the  frame  at  points  where 


many  timbers  meet.  Particular  atten- 
tion must,  furthermore,  be  given  to  the 
manner  of  connecting  the  beams  so  that 
there  shall  be  no  tendency  to  rise  at  the 
crown  under  the  action  of  the  varying 
load,  Figure  4  affords  an  illustration 
of  a  very  simple  method  of  arranging 
the  timbers  for  arches  of  small  span. 
The  inclined  struts  abut  against  horizon- 
tal straining  beams  placed  at  different 
points  on  the  soffit,  and  to  add  greater 
strength  to  the  framing,  and  to  prevent 
the  horizontal  beam  from  sagging,  bridle 
pieces  are  placed  in  the  direction  of  the 
radii  of  curvature.  The  chief  difficulty 
with  such  arrangement  as  this  is,  that 
as  they  require  beams  of  great  length 
they  can  be  used  to  advantage  only  in 
small  span  arches. 

The  centre  frames  for  the  Waterloo 
Bridge  over  the  Thames  were  construct- 
ed on  this  principle,  but  in  this  case  no 
horizontal  beams  were  used.  Under  the 
backpieces  were  placed  blocks  each  sup- 
ported by  two  inclined  struts  which 
made  equal  angles  with  the  radius  drawn 


58 


59 

through  the  centre  of  the  block.  In  a 
small  span  arch,  these  struts  would  have 
rested  on  framed  supports  placed  at  the 
opposite  abutments  of  the  arch  ;  but  in 
the  Waterloo  Bridge,  to  avoid  the  incon- 
veniences resulting  from  crossing  the 
struts,  and  of  building  beams  where  struts 
of  sufficient  length  could  not  be  obtain- 
ed from  single  beams,  the  ends  of  sev- 
eral struts  were  received  into  cast-iron 
sockets  placed  at  their  point  of  crossing 
and  suspended  by  bridle  pieces. 

Figure  5  is  a  good  design  for  a  cocket 
centre  of  large  span.  Here  the  C  F', 
H  F  and  D  d,  are  placed  in  the  direction 
of  the  radii  of  curvature  and  made 
double  ;  the  remaining  braces  are  single. 
In  determining  the  proper  dimensions 
for  the  scantling  of  such  a  frame,  we 
may  take  §  of  the  total  pressure  on  the 
arc  HH',  and  suppose  it  to  act  at  0  in 
the  direction  OF',  which  will  evidently 
be  the  greatest  load  this  timber  will  have 
to  sustain.  The  strain  upon  the  E  DF 
will  then  be  equal  to  J  the  load  on  B  H, 
and  that  on  H  F  as  \  D  C,  That  on  the 


61 

beams  E  F  and  F  Fr  is  to  be  found  from 
the  diagram  of  forces,  Fig.  5.  Here  hf 
which  is  in  the  direction  of  H  F  produc- 
ed, represents  the  pressure  on  this  beam; 
EA  is  drawn  parallel  to  EF,  and  ef 
parallel  to  F  F',  which  being  measured 
give  the  strain  on  EF  and  FF'  respec- 
tively. If  it  is  desirable  to  obtain  the 
dimensions  of  the  beams  with  great  ac- 
curacy we  may  use  the  following  formu- 
lae :  If  we  assume  the  relation  between 
the  breadth  and  depth  to  be  .6  to  1 
(which  is  an  excellent  proportion),  then 
for  an  inclined  beam  whose  angle  of  in- 
clination to  the  horizon  is  j3. 


0.6 
And  for  a  horizontal  beam 


(15) 


d  = 

0.6 

In  which  a  is  to  be  found  from  the  ex- 


• 

pression  —  . >  '^-£-±-=a,  in  which  b  is 
-L    W 

the  deflection  of  a  beam  whose  breadth 


62 

is  by  depth  is  J,  length  L,  and  load  W. 
For  pine  this  quantity  a  is  from  .0112  to 
.0105,  and  for  the  best  oak  .00934.  Eq. 
15  or  16  will  give  the  depth  in  inches. 
If  it  so  happens  that  the  value  of  a,  in 
the  above  equation,  cannot  be  obtained 
either  by  actual  experiment  or  from 
tables,  we  may  make  the  square  of  one 
side  equal  to  twice  the  square  of  the 
other,  which  will  give  a  ratio  of  7  to  5 
very  nearly,  and  use  the  equation 


cos  b 

Where  w  is  the  load,  I  the  length,  and  b 
the  angle  the  beam  makes  with  the  ver- 
tical, and  d  the  dimension  of  the  smaller 
side,  equal  f  of  the  larger.  In  centre 
frames,  however,  such  a  degree  of  exact- 
ness is  rather  unnecessary,  since,  by  al- 
lowing 1,000  Ibs.  to  the  square  inch  we 
can  obtain  the  cross  section  from  the 
load  with  all  the  accuracy  desirable  in 
practice. 

The  transversal  strain  on  any  one  back- 
piece  or  segment  of  the  rib  under  the 


63 

laggings  may  be  obtained  from  the  ex- 
pression 

S=P  sec  0      ...     (17) 

<f>  being  the  angle  the  backpiece  makes 
with  the  horizon,  and  P  the  vertical  com- 
ponent of  the  pressure  on  the  same  piece 
found  by  any  of  the  methods  already 
explained,  or  from 

.     .     .     (18) 

W  being  the  pressure  on  each  lineal  foot 
of  the  segment,  L  its  length  ;  r  the 
radius  of  curvature  at  the  point  in  ques- 
tion, x  the  distance  of  the  lower  end 
of  the  backpiece  from  the  vertical 
through  the  crown  of  the  arch  and  the 
centre  of  curvature,  and  h  the  distance 
between  the  two  ends  of  the  segment 
measured  vertically. 

The  strain  upon  any  one  of  the  lag- 
gings will  depend,  independent  of  the 
weight  of  the  arch  stones,  on  the  dis- 
tance of  the  ribs  from  centre  to  centre, 
the  place  the  lagging  occupies  in  the 
arch  and  the  manner  in  which  the  lag- 


64 

gings  are  attached  to  the  backpieces  of 
the  frame.  As  regards  the  latter  point, 
there  are  two  ways  of  making  them  fast 
to  the  rib.  They  may  be  placed  directly 
on  the  backpiece  and  nailed  to  it,  or  they 
may  be  mounted  on  folding  wedges 
placed  between  each  bolster  or  lagging 
and  «the  rib,  which  latter  arrangement 
will  be  considered  in  detail  when  we 
come  to  speak  of  the  striking  plate. 
The  bolsters,  moreover,  may  be  placed  on 
the  rib  in  such  wise  that  they  touch  each 
other,  or  may  be  separated  by  a  space 
equal  to  their  own  breadth.  The  former 
method  is  most  usually  resorted  to  in 
the  construction  of  brick  arches,  and  is 
illustrated  in  Fig.  4  ;  the  latter  is  used 
in  building  stone  arches,  and  is  illustrated 
in  Fig.  2.  By  separating  the  laggings 
in  this  wise  a  considerable  slving  of  tim- 
ber is  effected,  while  the  air  is  also  given 
freer  access  to  the  joints  of  the  arch  and 
the  mortar  much  sooner  dried.  When 
these  pieces  are  separated,  it  is  evident 
that  the  cross  section  of  each  must  be 
slightly  greater  than  when  they  are 


65 

placed  touching  each  other,  and  that  the 
section  of  the  laggings  placed  near  the 
crown  should  be  larger  than  those  near 
the  angle  of  repose.  This  latter  point 
is  not  worth  considering  in  practice  un- 
less the  arch  stones  are  very  heavy,  for 
in  arches  of  the  ordinary  span  and  weight 
the  saving  thus  effected  in  the  timber  is 
hardly  worth  the  labor  of  calculation. 
In  determining  the  proper  dimensions  of 
the  laggings,  it  is  sometimes  customary 
to  insure  against  any  deflection,  by  sup- 
posing the  entire  load  on  each  lagging  to 
act  at  its  middle  point  and  calculate  for 
a  beam  strained  in  this  manner. 

BRACING. 

It  is  to  be  observed  in  connection  with 
the  matter  of  bracing,  that  the  frames 
should  be  arranged  in  such  wise  that  no 
piece  suffers  any  strain  other  than  com- 
pression or  extension  in  the  direction  of 
its  length.  As  it  is,  however,  by  no 
means  an  easy  matter  to  make  the  dis- 
tinction, we  shall  give  the  following  rule 
to  which  there  is  no  exception  : 


Suppose  we  have  two  beams  abutting 
Against  each  other  at  their  upper  end, 
and  loaded  at  their  point  of  intersection 
with  a  weight.  Take  notice  of  the  direc- 
tion in  which  this  straining  force  acts,. 
and  from  the  point  at  which  it  acts 
draw  in  this  direction  a  line  representing 
by  its  length  the  intensity  of  the  strain. 
From  the  remote  end  of  this  line  draw 
lines  parallel  to  the  two  pieces  on  which 
the  strain  is  exerted.  The  line  drawn 
parallel  to  one  must  of  necessity  cut  the 
other  or  its  direction  produced.  If  it 
cut  the  beam  itself  the  piece  is  compress- 
edy  and  acts  as  a  strut.  If,  on  the  other 
hand,  it  cuts  the  direction  of  the  beam 
produced^  the  piece  is  stretched  and  acts 
as  a  tie.  We  may  then  lay  it  down  as 
a  general  rule  in  framing,  that  if  the 
piece  from  which  the  strain  comes  lies 
within  the  angle  formed  by  the  pieces 
strained,  the  strains  these  sustain  are  of 
the  opposite  kind  to  that  of  the  straining 
point ;  if  that  inputting,  they  are  push- 
ing ;  if  that  is  compressed  they  are 
stretched.  Again,  if  the  piece  from  which 


6V 

the  strain  comes  lies  within  the  angle 
formed  by  the  direction  of  the  two  pro- 
duced, all  will  have  the  same  kind  of 
strain  ;  and,  finally,  if  within  the  angle 
formed  by  the  direction  of  one  produced 
and  the  other  piece  itself  ',  the  strain  will 
be  of  the  same  kind  as  that  of  the  most 
remote  of  the  two  beams  strained,  and  of 
the  opposite  kind  to  that  of  the  nearest. 

The  object  of  all  bracing,  then,  being 
to  convert  all  transversal  strains  into 
others  which  act  in  the  direction  of  the 
length  of  the  beams,  the  frame  must  be 
divided  into  a  number  of  triangles  ;  for 
as  the  triangle,  or  some  modification  of 
it,  is  the  only  geometrical  figure  which 
possesses  the  property  of  preserving  its 
figure  unaltered  so  long  as  the  length  of 
its  sides  remain  constant,  it  is  the  figure 
best  suited  for  structures  in  which  rigid- 
ity is  essential  for  stability.  But,  again, 
some  forms  of  triangles  are  much  to  be 
preferred  to  others  ;  the  strength  of  the 
pieces  forming  the  triangle  depending 
very  much  on  the  angle  they  make  with 
each  other.  Oblique  angles  are  to  be 


68 

avoided.  Acute  angles  when  not  accom- 
panied by  oblique  are  not  so  injurious, 
because  the  strain  can,  in  such  pieces, 
never  exceed  the  straining  force  ;  but  in 
an  oblique  angle  it  can  surpass  it  to  any 
degree. 

In  all  forms  of  bracing,  too  much  at- 
tention cannot  be  given  to  the  joints. 
Where  the  beams  stand  square  with  each 
other,  and  the  strains  are  also  square 
with  the  beams  and  in  the  plane  of  the 
frame,  the  common  mortise  and  tenon 
is  the  most  perfect  joint,  a  pin  usually 
put  through  both  so  as  to  draw  the  tenon 
sight  into  the  mortise,  and  so  cause  the 
thoulder  to  butt  very  snugly.  Round 
pins  are  much  better  than  square  ones, 
as  they  are  not  liable  to  split  the  bit. 
Where  the  beams  are  very  oblique,  it  is 
difficult  to  give  the  foot  of  the  abutting 
one  such  a  hold  as  to  bring  many  of  its 
fibres  into  actual  contact  with  the  beam 
butted  on.  It  would,  in  such  case,  seem 
proper  to  give  it  a  deep  hold  with  a  long 
tenon.  Nothing,  however,  can  be  more 
injurious,  for  experience  has  fully  proved 


69 

that  they  are  very  liable  to  break  up  the 
wood  above  them  and  push  their  way 
along  the  beam.  For  instance,  suppose 
the  head  of  an  inclined  strut  abutting 
on  a  horizontal  beam  to  descend  a  little; 
the  angle  with  this  latter  beam  is  dimin- 
ished, by  the  strut  revolving  round  the 
stress  in  the  tie  beam.  By  this  motion 
the  bed  of  the  strut  becomes  a  powerful 
fulcrum  to  a  very  long  lever  ;  the  tenon 
is  the  other  arm  and  very  short.  It 
therefore  forces  up  the  wood  above  it  and 
slides  along  the  horizontal  beam.  This 
may  be  prevented  by  making  the  tenon 
shorter, and  giving  to  its  toe  a  shape  which 
will  make  it  butt  firmly  in  the  direction 
of  the  thrust,  on  the  solid  bottom  of  the 
mortise.  When  the  beam  is  a  tie  the 
joint  must  depend  for  its  strength  on  the 
pins  or  bolts,  and  the  iron  straps  placed 
across  it. 

STRIKING   THE    CENTRES. 

Undoubtedly  the  most  dangerous  opera- 
tion connected  with  the  use  of  bridge 
centres  is  the  process  of  striking  them. 


70 

No  matter  with  how  much  care  the  arch 
may  have  been  constructed,  the  drying 
and  squeezing  of  the  mortar  will  cause 
it  to  settle  in  some  degree  when  the  cen- 
tres are  removed,  and  this  degree  of 
settlement  seems  to  be  very  largely  af- 
fected by  the  time  the  centres  are  allow- 
ed to  stand.  By  some  it  has  been  urged 
that  the  centring  should  never  be  remov- 
ed until  the  mortar  in  the  joints  of  the  last 
course  has  had  ample  time  to  harden  ; 
others  going  to  the  other  extreme  have 
advocated  striking  the  ribs  as  soon  as  the 
arch  is  keyed,  claiming,  not  without 
some  reason,  that  the  settlement  of  a 
well  built  arch  will  never  be  so  great  as 
to  become  dangerous  even  though  the 
supporting  frames  be  removed  when  the 
mortar  is  green.  But  possibly  the  best 
practice  lies  not  far  from  either  of  these 
extremes.  It  has,  indeed,  time  and 
again,  been  amply  demonstrated  that  to 
leave  the  centring  standing  till  the  mor- 
tar has  hardened,  and  then  take  away  all 
support,  the  mortar  having  become  un- 
yielding, is  to  cause  the  courses  to  open 


11 

along  their  joints.  To  strike  the  centre, 
on  the  other  hand,  when  the  arch  is 
green  will,  seven  cases  out  of  ten,  be 
followed  by  the  fall  of  the  bridge  ;  but 
by  easing  the  centring  as  soon  as  the 
arch  is  keyed  in,  and  continuing  this 
gradual  easing  till  the  framing  is  quite 
free  from  the  arch,  the  latter  has  time 
to  settle  slowly  as  the  mortar  hardens, 
and  the  settlement  will  be  found  to  be 
very  small. 

It  becomes  necessary,  therefore,  to  pro- 
vide some  arrangement  by  which  the 
framing  may  be  slowly  lowered  from  the 
soffit  of  the  arch,  an  operation  accom- 
plished in  a  variety  of  ways  ;  by  folding 
or  double  wedges,  by  striking  plates,  by 
bearing  irons  and  screws,  by  cutting  off 
the  ends  of  the  principal  supports,  and, 
finally,  by  plate  iron  cylinders  filled  with 
sand.  The  folding  wedges  are,  perhaps, 
most  commonly  met  with  in  practice, 
and  are  finely  suited  for  arches  of  small 
span,  as  a  sill  stretching  from  abutment 
to  abutment  may  then  be  used  to  rest 
them  on.  They  consist  of  two  hard- 


72 

wood  wedges,  about  15  in.  long,  right 
angled  along  one  edge,  and  placed  one 
upon  the  other  in  such  wise  that  the 
thick  end  of  one  shall  be  over  the  thin 
end  of  the  other,  thus  making  their  sur- 
face of  contact  an  inclined  plane.  These 
wedges  are  placed  under  the  tie  beam  of 
the  rib  and  on  the  sill,  as  is  illustrated 
in  Fig.  2.  It  is  evident  that  by  driving 
the  upper  wedge  up  along  the  inclined 
surface  of  the  lower,  the  rib  which  rests 
upon  the  upper  one  must  rise,  so  that 
by  placing  a  number  of  these  folding 
wedges  under  each  rib  it  may  easily  be 
keyed  up  to  the  desired  level,  and  by 
driving  the  upper  down  the  inclined  sur- 
face of  the  lower,  the  rib  may  gradually 
be  lowered.  To  keep  the  under  wedge 
in  place,  it  is  usually  made  fast  to  the 
sill  and  the  surface  of  contact  of  each 
wedge  well  greased  with  soft-soap  and 
black  lead.  When  the  wedges  are  in 
place  under  the  rib,  it  is  a  good  practice 
to  mark  each  wedge  at  the  point  where 
contact  ceases,  so  that  when  the  centres 
are  being  lowered  we  may  be  able  to 


73 

know  whether  they  are  lowered  uniform- 
ly or  not.  For  instance,  let  the  lower 
wedges  of  three  pair  of  folding  wedges 
project  two  inches  beyond  the  end  of  the 
upper  ones,  and  mark  with  chalk  on  the 
side  of  each  lower  wedge  the  point 
where  contact  ceases;  namely,  two  inches 
from  its  end.  Now,  if  in  striking  the 
centres  the  upper  wedges  have  all  been 
driven  back  so  that  the  end  of  each  in- 
stead of  being  at  the  line  is  one  inch  be- 
yond it,  then  the  frame  has  been  uni- 
formly lowered  ;  but  if  some  are  one 
inch  and  some  f  inch  from  the  line,  the 
frame  has  not  been  lowered  uniformly, 
and  the  difference  must  be  corrected  by 
driving  all  the  wedges  till  they  are  one 
inch  from  the  chalk  line. 

It  is  evident  that  such  an  arrangement 
of  folding  wedges  can  be  of  but  little 
use  unless  the  horizontal  beam  or  sill  on 
which  they  rest  is  rigidly  supported  from 
beneath,  as  any  yielding  of  the  sill 
would  be  followed  by  a  separation  of 
the  wedges  and  rib.  In  constructing 
bridges  of  wide  span  over  creeks  or  riv- 


74 

ers  on  which  there  is  no  navigation  to  be 
interrupted,  it  is  usual  to  make  use  of 
the  folding  wedges  and  support  the  sill 
by  a  row  of  piles  driven  into  the  river 
bed,  and  it  then  becomes  especially  ne- 
cessary to  watch  the  wedges  lest  by 
some  settling  of  the  piles  and  sill  they 
have  separated  in  the  smallest  degree 
from  the  tie  beam  of  the  rib. 

In  cocket  centres  the  folding  wedges 
are  replaced  by  a  sriking plate  placed  at 
each  end  of  the  rib,  and  sustained  by 
strutting  or  raking  pieces  which  abut 
either  on  off-sets  at  the  foot  of  the  pier 
or  on  sills  placed  on  the  ground.  Each 
plate  consists  of  three  parts,  a  lower  and 
upper  plate  and  a  compound  wedge 
driven  between  them.  The  upper  of 
these  plates  is  of  wood  made  fast  to  the 
base  of  the  rib,  and  is  cut  into  a  series 
of  offsets  on  its  under  surface  (see  Fig. 
4).  The  lower  plate  is  likewise  of  wood 
cut  into  offsets,  but  on  its  upper  surface, 
and  is  firmly  attached  to  the  raking 
pieces  which  sustain  it.  The  compound 
wedge  consists  of  a  beam  cut  into  offsets 


75 

both  upon  its  upper  and* lower  sides  so 
as  to  fit  those  of  the  two  plates,  and 
when  driven  between  them  is  held  in 
place  by  keys  driven  behind  its  shoul- 
ders. 

Previous  to  the  time  of  Hartley,  the 
rib  was  struck  in  one  piece  by  the  use 
either  of  wedges  or  striking  plates.  To 
him,  however,  we  are  indebted  for  an 
improved  system  of  striking  or  easing 
the  centres  by  supporting  each  lagging 
upon  folding  wedges.  When  this  ar- 
rangement is  used  the  rib  is  firmly  at- 
tached to  its  supports,  and  the  laggings 
rest  upon  wedges  placed  between  them 
and  the  back  pieces  of  the  rib.  A  great 
advantage  gained  by  this,  is  that  the 
laggings  may  be  removed  course  by 
course  from  under  the  arch,  and  replaced 
if  the  settlement  prove  to  be  too  great 
at  any  one  part  of  the  soffit.  Another 
method,  at  one  time  much  in  use  among 
French  engineers,  is  to  cut  off  the  ends  of 
the  chief  supports  of  the  rib  piece  by 
piece,  an  operation  which  cannot  be  ac- 
complished with  much  regularity,  nor 
without  much  danger. 


76 

The  least  objectionable  way  of  strik- 
ing centres,  and  one  accomplished  with 
great  ease  and  regularity  is  by  the  use 
of  sand,  confined  in  cylinders.  A  num- 
ber of  plate  iron  cylinders  one  foot  high 
and  one  foot  in  diameter  are  placed  upon 
a  stout  platform  sustained  by  timber 
framing.  The  lower  end  of  each  cylin- 
der is  stopped  by  a  circular  disc  of  wood 
of  an  inch  thickness  fitting  tightly  into 
the  cylinder,  and  at  about  an  inch  above 
this  wooden  bottom  three  or  four  holes 
an  inch  each  in  diameter  are  drilled 
through  the  iron  sides  of  the  cylinder 
and  stopped  with  corks  or  plugs  of 
wood. 

Into  the  cylinders  thus  prepared  is 
poured  clean  dry  sand  to  a  height  of  9 
or  10  inches  above  the  bottom,  and  on 
this  sand  in  each  cylinder  rests  a  cylin- 
drical wooden  plunger,  which  fits  so 
loosely  as  to  work  with  ease,  and  forms 
one  of  the  vertical  supports  of  the  rib. 
To  prevent  moisture  getting  at  the  sand, 
the  joint  between  the  plunger  and  cylin- 
der is  filled  with  cement.  So  long  as  the 


77 

sand  is  dry  it  remains  incompressible  to 
any  weight  that  may  press  on  it,  and  the 
rib  is  thus  kept  invariably  in  its  place. 
When  the  centre  is  to  be  lowered,  the 
plugs  are  taken  out  of  the  cylinder,  and 
as  the  sand  runs  out  of  each  with  uniform 
velocity  the  frame  is  uniformly  lowered. 
This  method  is  of  especial  value  for  cen- 
tres of  great  weight. 

The  distance  at  which  the  frames  or 
ribs  of  centres  should  be  placed  apart, 
measuring  from  the  centre  of  one  rib 
to  that  of  the  next,  must  be  regulated 
solely  by  the  weight  of  stone  used  for 
the  arch,  the  distance  varying  inversely 
with  the  increase  of  weight.  That  is 
to  say,  if  we  assume  some  distance  for 
stones  of  a  given  weight,  say  6  feet  for 
stones  weighing  150  Ibs.  per  cubic  -yartt,  jp*TTf 
and  wish  to  find  the  proper  distance 
apart  of  the  ribs  when  the  stones  weigh 
but  120  Ibs.  per  cubic  y#F<L  we 


150  :  120*.  15:4.   Then  making  6  ft.  the 
distance  for  150  lb., 
4  :  5;  *.6  :  x     4  #=30     x—  7  ft.  6  in., 


78 

the  proper  distance  for  stones  of  12o 
Ibs.  per  cubic  -jSmL  The  following  table 
has  been  calculated  in  this  manner  : 

Weight  of  Stone  Distance  apart 

per  i  of  the 

Cubic  <¥*ed.  <T**f  Rib  of  Centring. 

120  Ibs....   7  ft.    6    in. 

125  Ibs 7  ft.    3    in. 

130  Ibs ; tf  ft.  11    in. 

135  Ibs 6  ft.    8    in. 

140  Ibs 6  ft.    5    in. 

145  Ibs 6  ft.    2    in. 

150  Ibs 6  ft.    0    in. 

155  Ibs  5  ft.  10    in. 

160  Ibs 5  ft.    7    in. 

165  Ibs 5  ft.    5    in. 

170  Ibs 5  ft.    3    in. 

175  Ibs .5  ft.    Hin. 

180  Ibs 5  ft.    0    in. 

185  Ibs 4  ft.  10J  in. 

190  Ibs ...4  ft.    8    in. 

195  Ibs 4  ft.    7    in. 

200  Ibs 4  ft.    1    in. 

It  now  remains  to  consider  briefly,  the 
subject  of  centring  as  used  in  the  con- 
struction of  the  arched  roofs  of  tunnels. 
In  work  of  this  description,  the  span 
being  always  small,  the  arch  light  and 


79 

the  facilities  for  obtaining  firm  points  of 
support  for  each  rib  as  great  as  can  be 
desired,  all  the  hindrances,  that  so  often 
make  the  framing  of  a  stone  bridge 
centre  a  matter  of  no  small  difficulty 
and  foresight,  are  wanting,  and  the  rib 
admits  of  a  simplicity  of  arrangement 
at  once  favorable  to  economy  of  mate- 
rial and  of  space.  It  must,  however,  be 
remembered  that  although  the  span  is 
small  and  the  arch  light,  the  strength  of 
the  rib  of  a  tunnel  centre  must  be  much 
greater  in  proportion  to  the  burden  it 
has  to  carry  than  that  of  a  bridge  cen- 
tre ;  since  the  former  has  not  only  to  re- 
sist the  weight  of  the  earth  above  it, 
but  must  also  withstand  the  wear  and 
tear  of  many  destructfui  causes  to  which 
the  latter  is  never  exposed.  In  tunnel- 
ing through  a  hill  side,  no  matter  how 
short  the  distance,  more  or  less  rock  will 
invariably  be  met  with,  and  more  or  less 
blasting  must  therefore  be  done,  and  the 
shock  and  flying  splinters  of  rock  which 
accompany  each  explosion  do  mucli  mis- 
chief to  the  ribs  by  disturbing  or  injur- 


80 

ing  them.  This  cause  acts  strongly  on 
all  parts  of  the  centre,  but  is  especially 
severe  with  the  leading  ribs,  which,  as 
the  brick  work  must  always  be  kept  well 
up  to  the  heading,  are  directly  exposed 
to  the  violence  of  each  explosion. 

A  second  cause  of  injury  to  the  ribs, 
and  one  quite  as  damaging  and  unavoid- 
able as  the  first,  is  the  repeated  taking 
down,  carrying  forward,  and  putting  up 
of  the  ribs  every  time  a  length  of  arch 
is  completed.  In  bridges,  unless  the 
structure  is  composed  of  a  series  of 
arches,  the  centring  is  never  disturbed 
from  the  time  it  is  first  put  up  until  it 
is  finally  struck  on  the  completion  of  the 
works.  In  tunneling,  however,  to  avoid 
the  foolish  expense  of  building  centres 
from  end  to  end  of  the  tunnel,  it  is  cus- 
tomary to  construct  but  one  length  of 
twelve  or  fifteen  feet  of  centring,  and  to 
move  this  forward  whenever  it  becomes 
necessary  to  turn  a  new  length  of  arch. 
Thus,  for  example,  we  will  suppose  that 
we  are  driving  a  tunnel  through  earth  of 
a  moderate  degree  of  heaviness,  and  are, 


81 

therefore,  using  centres  consisting  of  two 
sets  of  laggings  and  five  ribs,  two  made 
without  and  three  with  a  horizontal  tie 
beam.  The  object  in  making  some  of 
these  ribs  without  the  tie  beam  is  that, 
by  so  doing,  the  centring  may  be  brought 
close  up  to  the  heading  without  interfer- 
ing with  the  raking  props,  which  could 
not  be  done  were  the  beams  to  be  retain- 
ed. These  five  ribs  are  arranged  in 
practice  so  that  one  without  the  tie 
beam  shall  be  placed  at  each  end  of  the 
length  of  centring,  and  between  these 
two  are  the  three  with  beams.  We  will 
suppose  this  to  be  the  arrangement  of 
the  ribs  in  the  present  case,  and  will 
number  them,  beginning  with  that  near- 
est the  heading,  1,  2,  3,  4,  5.  While  the 
arch  is  being  turned  upon  this  length 
the  excavation  for  a  new  one  has  been 
made,  the  invert  built,  the  side  walls 
raised  to  springing  line  and  all  is  ready 
to  carry  forward  the  centring.  This 
operation,  however,  must  be  done  with 
the  utmost  caution.  If  the  ribs  are 
taken  from  under  the  newly  completed 


82 

arch  before  the  invert  and  side  walls  of 
the  advanced  length  are  built,  the  whole 
piece  of  arch  with  its  side  walls  will  be 
almost  certain  to  separate  from  the 
length  just  behind,  and  move  forward 
several  inches  in  the  direction  the  work 
is  progressing.  If, on  the  other  hand,  after 
the  advanced  side-walls  are  up,  all  the 
ribs  are  taken  from  under  the  arch,  this 
latter  will  be  quite  certain  to  come  down 
in  ruins,  since  it  has  to  uphold  not  only 
the  weight  of  the  earth  resting  imme- 
diately upon  its  bricks,  but,  in  addition, 
half  the  weight  of  the  earth  which  press- 
es upon  the  crown  bars  of  the  newly  exca- 
vated length,  as  one  end  of  all  these 
bars  rests  upon  the  arch  near  its  end. 
Rib  number  1,  then,  which  is  directly 
beneath  the  end  of  the  crown  bars,  can 
not  be  removed  with  any  degree  of  safe- 
ty. It  is  also  desirable  that  number  3 
should  be  left  in  place  to  help  support 
the  laggings.  Numbers  2,  4  and  5  are 
the  only  ribs  left,  and  these  are  to  be 
taken  down  and  set  up  forward,  taking 
care  that  5,  which  has  no  tie  beam,  is 


83 

placed  nearest  the  heading;  the  order  of 
arrangement  then  being  5,  4,  2,  1,  3. 

Over  the  rib  thus  arranged  a  second 
set  of  laggings  is  laid,  and  on  them  the 
arch  is  turned.  When  this  length  is 
completed,  and  all  preparation  made  to 
carry  forward  the  centring,  the  ribs  num- 
bered 4,  1,  3  are  taken  down  and  set  up 
forward  in  the  order  1,  3,  4,  5,  2,  and  so 
on  till  the  centring  reaches  the  end  of 
the  tunnel,  or  meets  that  coming  from 
the  opposite  end  of  the  tunnel,  suppos- 
ing it  to  be  worked  both  ways. 

Now,  it  is  precisely  this  continual  tak- 
ing down  and  setting  up  of  the  ribs, 
that  produces  so  much  injury  to  them, 
since,  in  order  to  pass  them  under  the 
forward  ribs  and  props  which  remain 
standing,  it  is  necessary  to  take  them  in 
pieces.  Each  rib,  therefore,  must  be 
framed  in  such  wise  that  it  may  be  re- 
peatedly taken  apart  and  put  together 
again  without  injury  to  its  strength  or 
to  the  joints  of  the  timbers  removed  and 
replaced.  Figs.  5  and  6  afford  an  illus- 
tration of  two  centre  ribr  wamrrvj  to 


84 

meet  these  requirements  in  the  simplest 
manner  possible.  Fig.  5  is  a  drawing  of 
a  leading  or  segment  rib,  which  it  will 
be  observed  is  constructed  without  a 
complete  tie  beam  at  the  bottom  so  as  to 
offer  no  obstruction  to  the  raking  props. 
It  consists  of  two  parts  or  segments, 
which,  when  the  rib  is  placed,  join  at 
the  crown  of  the  arch  and  along  the  line 
a  b,  and  are  made  fast  to  each  other  by 
two  iron  bars  placed  across  the  joint  at 
the  crown,  one  on  each  side  of  the  back- 
pieces,  and  bolted  through  the  back- 
pieces  as  shown  at  c  c.  An  additional 
band  is  passed  around  the  two  vertical 
beams  as  shown  at  d.  To  prevent  any 
slipping  of  these  beams  along  the  joint 
a  ^  the  surface  of  each  beam  is  notched, 
as  shown  at  e,  and  a  wedge  driven 
through  the  notch.  When  the  rib  is  to 
be  taken  down,  the  band  at  c  c  and  that 
at  d  is  removed,  and  the  wedge  at  e 
driven  out,  and  the  rib  thus  separated 
into  two  segments  may  be  carried 
through  a  comparatively  small  space. 
As  this  leading  rib  is  subjected  to  the 


85 

direct  effects  of  the  blasts,  and  to  flying 
fragments  of  rocks,  its  joints  must  be 
strengthened  by  irons  placed  on  each 
side  of  the  rib,  over  the  joint,  and  bolt- 
ed through  the  timbers  as  shown  in  the 
figure. 

This  form  of  rib  is  finely  adapted  for 
tunnel  centring,  as  it  may  be  taken  apart 
without  removing  a  single  beam,  while 
its  joint  is  so  arranged  that  the  pressure 
of  the  arch  assists  in  no  small  degree  to 
hold  its  parts  in  place.  Indeed,  the  only 
valid  reason  why  this  form  of  rib  should 
not  be  used  in  every  part  of  a  tunnel 
centre  is  the  absence  of  the  tie  beam, 
which  is  certainly  a  great  security  against 
the  spreading  or  contracting  of  the  span. 
Were  this  tie  beam  supplied,  and  it  may 
easily  be  supplied  by  an  iron  screw  rodr 
this  form  of  frame  would  probably,  in 
addition  to  the  convenience  of  taking 
apart  and  resetting,  sustain  any  amount 
of  pressure  ever  likely  to  occur  either 
vertically  or  laterally,  as  also  all  ordi- 
nary wear  and  tear  from  use. 

Fig.   6  represents  one  of  the  interme- 


86 


87. 

diate  ribs  called  scarf  or  queen  post  cen- 
tres, which,  as  there  are  no  props  to  be 
interfered  with,  are  provided  with  hori- 
zontal tie  beams.  As  these  ribs  are  also 
to  be  taken  apart  each  time  they  are 
shifted,  the  tie  beam  is  composed  of  two 
beams  joined  by  a  scarf  joint  strenthen- 
ed  by  a  piece  of  timber  placed  above  it, 
and  bound  to  the  tie  by  two  bands  of 
iron  as  shown  in  the  figure.  The  hori- 
zontal beam  joining  the  queen  posts  is 
also  movable,  and  is  held  in  place  by 
the  iron  placed  over  its  joints  and  bolt- 
ed through.  In  joints  thus  protected, 
the  holes  through  which  the  bolts  pass 
are  liable  after  a  time  to  become  so  much 
enlarged,  from  the  repeated  driving  in 
and  out  of  the  bolts,  so  as  to  injure  the 
strength  of  the  joint.  This  may  read- 
ily be  overcome  by  using  a  bolt  with 
screw  threads  at  each  end  in  place  of  a 
bolt  with  a  head  and  one  nut,  so  that 
when  once  driven  through  the  beam  it 
need  not  be  removed. 

By  a  comparison  of  these  two  forms 
of  ribs,  it  is  evident  that  while  the  queen 


88 

post  centre  possesses  an  advantage  over 
the  segment  form  in  that  it  is  not  liable 
to  lateral  spread,  it  is  at  the  same  time 
inferior  to  the  former  in  many  important 
points.  It  cannot  so  well  resist  shocks 
or  side  blows,  and  being  so  taken  to 
pieces  every  time  it  is  moved  is  very  lia- 
ble to  be  injured  especially  at  the  scarf 
joint.  An  additional  recommendation 
for  centres  constructed  on  the  plans  of 
Figs.  5  and  6,  is  the  small  amount  of  ma- 
terial used,  which  is  quite  as  small  as  is 
consistent  with  the  varying  strains  the 
ribs  are  exposed  to,  and  is  so  cut  that 
the  timbers  are  almost  as  valuable  when 
the  tunneling  is  completed  as  they  were 
when  first  purchased  for  the  ribs. 

The  estimation  of  the  dimensions  prop- 
er to  give  each  tie  and  brace  of  the  rib 
is  easily  determined  in  so  simple  an  ar- 
rangement, by  any  of  the  methods  given 
for  bridge  centres.  It  is,  however,  to 
be  remembered  that,  while  the  bridge 
centre  has  to  sustain  but  the  weight  of 
the  arch  stones  and  bonding  mortar,  a 
load  which  can  be  calculated  to  a  pound 


89 

before  one  stone  is  laid,  the  centring  of 
a  tunnel  has  to  resist  the  pressure  not 
only  of  the  brick  roof,  but  also  of  the 
earth  above,  and  that  this  latter  pressure 
is  wonderfully  variable.  The  pressure  of 
the  brick  work  will  of  course  vary  when 
laid  in  cement  and  when  laid  in  mortar. 
From  the  most  careful  experiments  made 
to  determine  the  weight  of  a  cubic  yard 
of  brick  work,  we  find  that  when  the 
bricks  are  laid  with  cement  the  weight 
per  cubic  yard  is  2,897  pounds,  or  in 
round  numbers  2,900  Ibs.;  when  laid  in 
mortar  beds  the  weight  falls  to  2,677,  a 
difference  of  some  220  Ibs.  per  cubic  yard. 
It  is  true  that  the  pressure  of  the  earth 
does  not  act  to  any  great  extent  on  the 
centring,  until  the  arch  is  turned  and  the 
crown  bars  drawn  forward  to  form  the 
roofing  of  the  newly  excavated  length, 
but  when  this  is  done,  and  the  three  ribs 
removed  to  be  set  up  in  advance,  the 
pressure  on  the  two  ribs  remaining  under 
the  arch  is  quite  severe.  This  load  is 
especially  variable  with  the  leading  or 
segment  ribs,  which  it  will  be  remember- 


90 

ed  are  placed  at  the  ends  of  the  length 
of  arch,  and  sustain  one  end  of  all 
the  side  and  crown  bars  supporting  the 
earth,  and  the  movement  which  this 
earth  is  at  any  moment  liable  to  take, 
cannot  be  foreseen.  At  times  a  whole 
length  can  be  gotten  out  and  the  arch 
turned  without  any  perceptible  motion 
of  the  earth  either  at  the  sides  or  on  top; 
at  others,  the  earth  will  of  a  sudden  be- 
gin to  move  and  throw  all  its  pressure 
on  the  side  bars  ;  then,  again,  the  action 
will  take  place  at  the  crown  and  become 
so  great  as  to  press  the  bars  down  in  the 
middle  through  a  distance  of  many 
inches,  or  even  to  break  the  stoutest  15- 
inch  oak  beams. 

This  action  of  the  earth,  however, 
seems  to  be  controlled  by  law,  since  it 
depends  largely  on  the  depth  of  the  tun- 
nel below  the  surface.  The  pressure  on 
the  sides  is  most  severe  in  those  parts  of 
the  tunnel  which  are  deepest,  and  the 
vertical  or  crown  pressure  (and  this  is 
always  the  severer  of  the  two)  where 
the  distance  below  ground  is  less.  At 


91 

• 

first  thought  this  is  precisely  the  reverse 
of  what  we  should  expect  to  be  the  case, 
for  it  seems  but  natural  tosuppose  that  the 
greater  the  depth  of  earth  the  greater  the 
pressure  on  the  arch  beneath.  The  facts 
are,  however, quite  the  contrary.  Thus,for 
example,  in  excavating  a  tunnel  through 
a  hill,  as  we  enter  the  hill  side  the  press- 
ure is  almost  exclusively  at  the  crown 
and  very  severe;  as  the  work  progresses 
nearer  and  nearer  the  centre  of  the  hill 
where  the  amount  of  earth  above  the 
arch  is  greatest,  the  vertical  is  changed 
to  lateral  pressure,  and  this  latter  is  in 
turn  changed  to  vertical  as  we  approach 
the  other  end.  This  is  well  accounted 
for,  by  supposing  that  in  the  former  case 
the  depth  of  earth  being  small,  the  whole 
of  it  gets  into  motion  and  acts  vertically 
downwards,  while  in  the  latter  case  the 
amount  of  earth  being  great  only  a 
small  portion  is  put  in  motion. 

The  leading  rib,  then,  must  be  con- 
structed with  no  small  care,  and  its  joints 
well  strengthened.  For  tunnels  of  ordi- 
nary span,  whatever  may  be  the  curve 


92 

of  soffit,  we  may  with  safety  give  the 
parts  the  following  dimensions.  The 
backpieces  two  thicknesses  of  3  in.  plank; 
the  planks  breaking  joints  with  each 
other.  For  the  segment  rib  make  all 
the  braces  6  in.  X  6  in.  ;  the  long  struts 
reaching  from  the  half  sills  to  the  crown 
7  in.  X  6  in.,  and  the  vertical  pieces  at 
the  crown  forming  the  joint  a  b  also 
7  in.  X  6  in-  F°r  the  queen  post  centres, 
make  the  tie  beam  9  in.  X  6  in->  as  a^8° 
the  short  timber  placed  over  the  scarf 
joint  ;  the  queen  posts  6  in.  X  6  in»>  ex> 
cepting  at  the  upper  and  lower  ends 
where  the  braces  abut  which  should  be 
10^  in.  X  6  m-  5  tf16  short  piece  between 
the  queen  posts,  and  just  below  the 
crown  4  in.  X 6  m->  and,  finally,  the 
braces  6  in.  X  H  in- 

The  manner  of  setting  the  ribs  is  il- 
lustrated in  Figs.  5  and  6.  Under  the 
queen  post  ribs  is  placed  a  long  horizon- 
tal beam,  its  two  ends  resting  on  the 
side  walls  and  supported  immediately 
under  the  foot  of  each  queen  post  by 
vertical  posts.  Upon  this  beam  are 


93 

placed  longitudinally  four  thick  planks, 
and  on  these  rest  the  folding  wedges. 
The  segment  ribs  are  supported  in  much 
the  same  way,  each  rib  by  two  short 
timbers,  one  end  of  each  resting  on  the 
side  walls  and  one  on  a  vertical  post 
under  the  heel  of  the  rib  ;  on  these  rest 
the  longitudinal  planks  which  are  placed, 
however,  a  little  oblique  to  the  tunnel 
since  the  heel  of  the  segment  rib  is  not 
so  far  from  the  wall  as  the  foot  of  the 
queen  post. 

It  has  already  been  remarked  that  it 
is  never  wise  to  strike  the  centres  until 
the  side  walls  of  the  newly  excavated 
length  are  up,  as  in  work  of  this  class 
there  is  a  strong  tendency  to  move  for- 
ward in  the  direction  of  the  excavation. 
If,  however,  the  ribs  are  struck  in  the 
manner  already  described,  with  the  lag- 
gings of  the  back  length  kept  tight  up 
to  the  arch  by  the  two  frames  left  under 
them,  we  shall  always  have  two  lengths 
of  completed  work  remaining  with  their 
supports,  not  only  until  the  next  length 
is  excavated  but  till  the  side  walls  are 


94 

built  and  ready  for  the  ribs.  Under 
such  circumstances  each  length  is  well 
able  to  uphold  its  burden  till  it  receives 
assistance  from  the  next  advancing  one, 
the  construction  of  which  to  springing 
line  occupies  several  days,  and  the  ce- 
ment or  mortar  has  time  to  harden  be- 
fore the  weight  comes  upon  the  arch 
after  striking  the  centring.  When,  how- 
ever, from  false  motives  of  economy, 
only  three  ribs  and  one  set  of  laggings 
are  used,  the  entire  support  of  one 
stretch  of  arch  must  be  removed  before 
another  can  be  commenced,  and  this, 
again,  before  a  third  is  turned,  leaving 
the  green  arch  unsustained.  in  which 
state  it  is  liable  to  give  way,  the  bricks 
to  crush  and  the  whole  arch  to  come 
down  in  utter  ruin.  Nowhere,  indeed, 
among  all  the  variety  of  engineering 
works  will  a  penny  wise  economy  more 
surely  prove  a  pound  foolish  one  than 
here ;  nowhere  else  will  an  unwise  sav- 
ing lead  to  so  profuse  an  outlay. 

Tunnel  centres  again  differ  from  those 
of  bridges  in  that  the  laggings  are  very 


95 

differently  adjusted.  In  the  later  case 
it  is  the  custom  in  practice  to  place  all 
the  laggings  on  the  ribs  before  commenc- 

OO         O 

ing  to  turn  the  arch,  by  which  means  no 
small  degree  of  stability  is  given  to  the 
ribs.  In  tunneling,  however,  where  only 
a  few  inches  of  space  remains  between 
the  backpieces  of  the  frame  and  the  pol- 
ing which  sustains  the  earth,  it  would  be 
utterly  impossible  to  turn  the  arch  if  all 
the  laggings  were  put  in  place  before 
the  brickwork  is  begun.  To  overcome 
this  difficulty,  only  a  few  laggings,  say 
five  or  six  are  placed  at  a  time.  Thus, 
starting  at  the  springing  line,  we  adjust 
six  laggings  on  each  side  of  the  frame, 
and  carry  the  arch  up  equally  on  both 
sides.  When  it  has  reached  the  upper 
bolster,  we  add  six  more,  and  the  mason- 
ry continued  as  before,  and  proceed  in 
this  way  until  very  near  the  crown  as 
shown  in  Fig.  7,  where  A  A!  is  the  brick 
work.  At  this  stage  of  the  work  the 
two  laggings  C  C'  are  placed  on  the  ribs, 
the  top  of  their  inner  edges  being  first 
rabbeted  as  shown  in  the  figure.  In 


9(3 


97 

these  rabbets  "cross"  or  "keying-in" 
laggings  B,  consisting  of  stout  planks 
18  or  20  inches  in  width,  are  laid  one  at 
a  time  beginning  at  one  end  of  the  cen- 
tring. The  bricklayer  whose  duty  it  is 
to  key-in  the  arch  stands  with  his  head 
and  shoulders  between  the  brickwork 
A,  A,  and  starting  at  the  end  of  the  last 
piece  of  completed  arch  places  the  first 
cross  lagging,  and  keys  in  the  arch  over 
it ;  then  a  second,  and  in  like  manner 
keys  in  the  arch  over  it,  and  thus  re- 
treats along  the  entire  opening  until  the 
whole  length  of  arch  is  keyed  in. 

Among  the  varieties  of  patent  centres 
that  planned  by  Mr.  Frazer,  affords  a 
most  excellent  specimen,  and  both  from 
its  strength,  economy,  ease  of  shifting 
and  the  small  amount  of  space  it  occu- 
pies in  the  tunnel,  has  met  with  much 
approval  from  the  engineering  profession 
in  England.  This  centre  consists  of  but 
three  ribs  each  differing  from  the  other 
two  in  design  as  shown  in  Figs.  9,  10 
and  11,  of  which  9  is  the  leading,  10  the 
middle  and  1 1  the  back  rib.  Each  rib  is 


98 


FIG.  9. 


FIG.  8. 


99 

constructed  of  four  pieces  of  timber  four 
and  one  half  in.  thick  by  16  inches  wide, 
scarfed  together  as  shown  in  the  draw- 
ings. In  centres  of  the  ordinary  con- 
struction, the  ribs  when  the  laggings 
are  laid  upon  them  are  all  of  precisely 
the  same  size,  and  of  the  same  span  and 
rise  as  the  soffit  of  the  intended  arch. 
In  Mr.  Frazer's  plan,  however,  all  the 
ribs  differ  in  the  length  of  their  radii ; 
the  Radius  of  the  outer  curve  of  the  lead- 
ing rib  (Fig.  9)  being  greater  ;  that  of 
the  middle  3  inches  less  than,  and  that  of 
the  back  rib  yet  smaller  than  the  radius 
of  the  soffit ;  so  that  the  middle  centre 
is  the  only  one  of  the  three  which  acts  in 
the  same  way  as  the  ordinary  centre 
frame,  that  is  to  say  with  the  laggings 
and  arch  resting  immediately  upon  the 
rib,  and  is  consequently  with  the  lag- 
gings on  it  of  the  same  rise  and  span  as 
ahe  arch. 

The  leading  rib  has  for  its  outlet  edge 
a  radius  12^  inches  larger  than  that  of 
the  arch  soffit,  and  for  its  inner  edge  one 
3^  inches  less  than  the  same  radius  (thus 


100 

making  the  16  in.  thickness)  and  is 
plated  on  *  both  the  inner  and  outer  sur- 
face with  half  inch  iron  plates  bolted 
quite  through.  The  plate  on  the  inner 
surface  is  six  inches  broad  and  projects 
2  inches  over  that  side  of  the  rib  which 
is  turned  towards  the  middle  rib,  thus 
forming  a  flange  on  which  the  laggings 
rest  (see  Fig.  9).  When  this  rib  then 
is  in  place,  it  must  be  its  whole  thickness 
in  advance  of  the  end  of  the  intended 
arch,  and  as  it  stands  12^  inches  above 
the  soffit  will  cover  12^  inches  of  the 
toothing  ends  of  the  brickwork,  thus 
forming  a  sort  of  mould  to  guide  the 
toothing. 

The  middle  rib  (Fig.  10)  is  also  covered 
on  the  under  surface  with  half  inch  plate 
iron  in  one  piece  and  bolted  through  as 
shown  in  figure,  thus  giving  the  rib  the 
strength  it  would  have  if  supported  by 
the  usual  struts  and  braces.  The  lag- 
gings rest  immediately  upon  the  upper 
surface  of  the  rib,  and  therefore  the 
radius  of  this  side  must  be  the  same  as 
that  of  the  arch  soffit,  less  three  inches  to 
allow  for  the  thickness  of  the  laggings. 


Fift.  10. 


FIG.  11. 


*    102 

The  back  rib  (Fig.  11)  is  covered  on 
the  under  surface  with  a  coating  of  half 
inch  plate  iron  an  one  piece,  which  is 
bolted  through  as  in  the  case  of  the  mid- 
dle rib.  Between  each  bolt  a  hole  is 
made  quite  through  the  rib  and  its 
plating,  and  in  it  is  placed  the  stem  of 
a  bearing  iron.  There  are  as  many  of 
these  irons  as  there  are  laggings,  the  ob- 
ject of  using  them  being  to  support  the 
laggings  which  it  will  be  observed  do 
not  rest  on  the  rib  but  on  the  projecting 
irons.  The  amount  of  projection  is  regu- 
lated by  means  of  adjusting  screws,  by 
screwing  which  the  laggings  may  be 
raised  to  the  required  level,  or  by  un- 
screwing lowered  one  by  one  from  the 
arch  when  completed.  These  last  two 
ribs  are  permanently  attached  to  trestling 
by  brackets,  straps  and  bolts,  and  the 
trestling  in  turn  mounted  on  iron  rollers 
which  run  on  half  timbers  laid  longitud- 
inally as  a  kind  of  tramway.  They  are 
also  steadied  at  the  crown  by  long  iron 
hooks  attached  to  one  rib  and  fitting  into 
eyes  in  the  other. 


103 

The  leading  rib  is  supported  upon 
slack  blocks  placed  on  top  the  brick- 
work of  the  side  walls  and  by  the  prop 
A.  This  prop,  to  allow  for  any  inequali- 
ties of  the  invert  on  which  it  rests,  is 
mounted  at  the  lower  end  on  a  screw  by 
which  it  may  be  raised  or  lowered. 

In  setting  this  patent  centre,  the  lead- 
ing rib  is  first  brought  forward  into  place 
and  wedged  up  on  the  edge  of  the  brick- 
work to  its  desired  level,  and  the  prop  A 
screwed  up  tight  under  the  heel.  The 
trestles  bearing  the  middle  and  back 
ribs  are  then  rolled  forward  till  the  mid- 
dle rib  is  at  the  proper  distance  from  the 
leading  one.  Three  pairs  of  wedges  are 
then  placed  between  the  bottom  piece  of 
the  trestles  and  the  tramway,  and  the 
trestles  thus  wedged  up  until  the  top  of 
the  middle  rib  is  on  a  level  with  the 
flange  of  the  leading  one,  thus  giving  two 
level  bearings  for  the  laggings.  The 
bearing  irons  of  the  back  rib  are  then 
pushed  out  by  the  adjusting  screws  until 
the  top  of  each  of  them  is  also  on  a  level 
with  the  flange  of  the  leading  rib.  The 


104 

three  bearings  then,  of  each  lagging, 
when  the  ribs  are  thus  arranged  is  first 
upon  the  flange  of  the  leading  rib,  then 
upon  the  middle  rib  itself,  and  finally 
upon  the  bearing  irons  of  the  back  rib. 
When  this  centre  is  to  be  again  moved 
forward  on  the  completion  of  this  length 
of  arch,  a  fourth  rib  called  the  "jack 
rib  "  is  first  fixed  under  the  laggings  in 
the  rear  of  the  back  rib,  this  last  named 
rib  consists  simply  of  a  band  of  iron  1 
inch  thick  by  2 \  wide,  bent  into  the  shape 
of  the  arch.  Opposite  every  alternate 
joint  of  the  laggings  a  screw  passes 
through  the  rib,  and  is  furnished  on  its 
outer  end  with  a  square  head  similar  to 
that  of  the  bearing  plates  of  the  back 
rib,  and  on  its  inner  or  lower  end  is  a 
loop  so  that  it  may  be  easily  turned  with 
a  lever.  The  object  of  placing  these 
screws  opposite  each  alternate  joint  is 
that  by  this  arrangement  only  half  as 
many  screws  are  needed  as  there  are 
laggings.  The  jack  rib  is  itself  support- 
ed at  each  end  by  an  iron  bar  2  feet 
long  driven  temporarily  into  the  wall. 


105 

As  soon  as  this  latter  rib  is  adjusted 
to  take  the  ends  of  the  laggings,  the 
wedges  are  driven  from  under  the  tres- 
tles and  its  rollers  thus  brought  down 
upon  the  tramway  prepared  for  them. 
When  thus  lowered,  it  is  evident  that 
the  two  ribs  (middle  and  back)  will  be 
so  much  below  the  leading  rib  which  is 
left  standing  that  they  will  easily  pass 
under  it.  The  trestle  and  its  ribs  is  then 
moved  forward  until  the  back  rib  is 
within  8  inches  of  the  ends  of  the  lag- 
gings, when  it  is  wedged  up  as  before. 
The  bearing  screws  are  then  screwed  up 
tight  against  the  laggings,  giving  these 
latter  the  same  support  hitherto  obtained 
from  the  leading  rib,  which  now  stands 
between  the  middle  and  back  rib.  The 
wedges  under  the  ends  of  the  leading 
rib  (see  Fig.  9)  are  then  removed  and 
the  rib  carried  forward  over  the  top  of 
the  middle  rib  and  adjusted,  as  previously 
described,  on  the  top  of  the  newly  built 
side  walls.  The  laggings  are  then  drawn 
forward  one  or  two  at  a  time  as  they  are 
needed,  beginning  at  the  springing  line. 


106 

The  great  advantage  which  these 
patent  centres  appear  to  possess  over 
those  of  the  ordinary  construction,  is  the 
total  absence  of  all  struts,  ties  and  braces, 
thus  leaving  a  fine  open  space  for  the 
scaffolding  and  materials  of  the  masons. 
The  amount  of  repairs  also  is  very  trivial, 
as  they  are  not  so  liable  to  be  injured  by 
flying  rocks.  In  point  of  economy, 
though  the  first  cost  of  patent  centres  is 
much  greater  than  that  of  the  segment 
or  queen  post  centres,  the  amount  expend- 
ed in  repairing  the  latter  soon  makes  up 
the  difference.  In  point  of  strength,  it 
must  be  acknowledged  that,  when  work- 
ing through  heavy  earth,  the  patent  cen- 
tre of  three  ribs  is  by  no  means  so  reli- 
able as  the  all-wood  centre  of  five  ribs 
and  two  sets  of  laggings,  used  as  above 
described.  And  this  is  certainly  a  seri- 
ous objection  in  that,  it  is  impossible  to 
tell  beforehand  at  what  moment,  owing 
to  a  fault  or  to  the  displacement  of  the 
local  beds,  the  character  of  the  earth  may 
change  completely  from  a  light  soil  to 
one  of  great  heaviness. 


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late  W.  H.  King,  U.  S.  Navy.     Revised  by  Chief 
Engineer  J.  W.  King, 
enlarged.     8vo,  cloth 


.      .  ,      .     .  . 

Engineer  J.  W.  King,  U.  S.  Navy.    Twelfth  edition, 


MINIFIE  (Wm.)    Mechanical  Drawing.    A  Text-Book 
4>f  Geometrical  Drawing  for  the  use  of  Mechanic! 

4 


L.  VAN  NOSTRAND'S  PUBLICATIONS. 

ana  Schools,  in  which  the  Definitions  and  Rules  ol 
Geometry  are  familiarly  explained;  the  Practical 
Problems  are  arranged,  from  the  most  simple  to  the 
more  complex,  and  in  their  description  technicalities 
are  avoided  as  much  as  possible.  With  illustrations 
for  Drawing  Plans,  Sections,  and  Elevations  of  Rail- 
ways and  Machinery ;  ah  Introduction  to  Isometrical 
Drawing,  and  an  Essay  on  Linear  Perspective  and 
Shadows.  Illustrated  with  over  200  diagrams  en- 
graved on  steel  By  Wm.  Minifie,  Architect  Sev- 
enth edition.  With  an  Appendix  on  the  Theory  and 

Application  of  Colors,     i  vol.  8vo,  cloth $4  oo 

.•'It  is  the  best  work  on  Drawing  that  we  have  ever  seen,  and  1« 
especially  a  text-book  of  Geometrical  Drawing  lor  the  use  of  Mechanics 
and  Schools.  No  young  Mechanic,  such  as  a  Machinists,  Engineer,  Cabi- 
net-maker, Millwright,  or  Carpenter,  should  be  without  it."— Scientific 
American. 

,  .  Geometrical  Drawing.  Abridged  from  the  octavo 
edition,  for  the  use  of  Schools.  Illustrated  with  48 
steel  plates.  Fifth  edition,  i  voL  xarno,  cloth....  2  oc 
STILLMAN  (Paul.)  Steam  Engine  Indicator,  and  the 
Improved  Manometer  Steam  and  Vacuum  Gauges— 
their  Utility  and  Application.  By  Paul  Stillman. 

New  edition,     i  vol.  lamo,  flexible  cloth i  oo 

SWEET  (S.  H.)  Special  Report  on  Coal ;  showing  its 
Distribution,  Classification,  and  cost  delivered  over 
different  routes  to  various  points  in  the  State  of  New 
York,  and  the  principal  cities  on  the  Atlantic  Coast. 

By  S.  H.  Sweet.    With  maps,  i  vol.  8vo,  cloth 3  oo 

WALKER  (W.  H.)  Screw  Propulsion.  Notes  on 
Screw  Propulsion  :  its  Rise  and  History.  By  Capt. 

W.  H.  Walker,  U,  S.  Navy,     i  vol.  8vo,  cloth 75 

WARD  (J.  H.)  Steam  for  the  Million.  A  popular 
Treatise  on  Steam  and  its  Application  to  the  Useful 
Arts,  especially  to  Navigation.  By  J.  H.  Ward, 
Commander  U.  S.  Navy.  New  and  revised  edition. 

i  vol.  8vo,  cloth i  oo 

WEISBACH  (Julius).    Principles  of  the  Mechanics  of 
Machinery  and  Engineering.     By  Dr.  Julius  Weis-  f 
bach,  of  Freiburg.    Translated  from  the  last  German 
edition.    ;  Vol.  I.,  8vo,  cloth 10  o« 


D.  VAN  NOSTBAND'S  PUBLICATIONS. 

DIEDRICH.  The  Theory  of  Strains,  a  Compendium 
for  the  calculation  and  construction  of  Bridges,  Roofs, 
and  Cranes,  with  the  application  of  Trigonometrical 
Notes,  containing  the  most  comprehensive  informa- 
tion in  regard  to  the  Resulting  strains  for  a  perman- 
ent Load,  as  also  for  a  combined  (Permanent  and 
Rolling)  l.oad.  In  two  sections,  adadted  to  the  re- 
quirements of  the  present  time.  By  John  D'edrich, 
0.  E.  .Illustrated  by  numerous  plates  and  diagrams. 
8vo,  doth 5  oo 

WILLIAMSON  (R.  S.)  On  the  use  of  the  Barometer  on 
Surveys  and  Reconnoissances.  Part  I.  Meteorology 
in  its  Connection  with  Hypsometry.  Part  II.  Baro- 
metric Hypsometry.  By  R.  S.  Wiliamson,  Bvt, 
Lieut.-Col.  U.  S.  A.,  Major  Corps  of  Engineers. 
With  Illustrative  Tables  and  Engravings.  Paper 
No.  15,  Professional  Papers,  Corps  of  Engineers, 
i  vol.  4to,  cloth 15  oo 

POOK  (S.  M.)  Method  of  Comparing  the  Lines  and 
Draughting  Vessels  Propelled  by  Sail  or  Steam. 
Including  a  chapter  on  Laying  off  on  the  Mould- 
Loft  Floor.  By  Samuel  M.  Pook,  Naval  Construc- 
tor, i  vol.  8vo,  with  illustrations,  cloth 500 

ALEXANDER  (J.  H.)  Universal  Dictionary  of 
Weights  and  Measures,  Ancient  and  Modern,  re- 
duced to  the  standards  of  the  United  States  of  Ame- 
rica. By  J.  H.  Alexander.  New  edition,  enlarged, 
i  vol.  8vo,  cloth -. 3  50 

WANKLYN.  A  Practical  Treatise  on  the  Examination 
of  Milk,  and  its  Derivatives,  Cream,  Butter  and 
Cheese.  By  J.  Alfred  Wanklyn,  M.  R.  C.  S.,  iamo, 
doth • • i  oo 

RICHARDS'  INDICATOR.  A  Treatise  on  the  Rich- 
ards Steam  Engine  Indicator,  with  an  Appendix  by 
F.  W.  Bacon,  M.  E.  i8mo,  flexible,  cloth i  m 

6 


D.  VAN  NOSTRAND'S  PUBLICATIONS, 

POPE.  Modern  Practice  of  the  Electric  Telegraph.  A 
Hand  Book  for  Electricians  and  operators.  By  Frank 
L.  Pope.  Eighth  edition,  revised  and  enlarged,  and 

fully  illlustrated.     Svo,  doth $2.00 

"  There  is  no  other  work  of  this  kind  in  the  English  language  that  con- 
tains in  so  small  a  compass  so  much  practical  information  in  the  appli- 
cation of  galvanic  electricity  to  telegraphy.  It  should  be  in  the  bands  of 
erery  one  interested  in  telegraphy,  or  the  use  of  Batteries  for  other  par- 
poses." 

MORSE.  Examination  of  the  Telegraphic  Apparatus 
and  the  Processes  in  Telegraphy.  By  Samuel  F. 
Morse,  LL.D.,  U.  S.  Commissioner  Paris  Universal 
Exposition,  1867.  Illustrated,  Svo,  cloth $2  oo 

SABINE.  History  and  Progress  of  the  Electric  Tele- 
graph, with  descriptions  of  some  of  the  apparatus. 
By  Robert  Sabine,  C.  E.  Second  edition,  with  ad- 
ditions, i2mo,  cloth x  35 

BLAKE.  Ceramic  Art.  A  Report  on  Pottery,  Porce- 
lain, Tiles,  Terra  Cotta  and  Brick.  By  W.  P.  Blake, 
U.  S.  Commissioner,  Vienna  Exhibition,  1873.  Svo, 
doth a  oo 

BENET.  Electro-Ballistic  Machines,  and  the  Schultz 
Chronoscope.  By  Lieut -Col.  S.  V.  Benet,  Captain 
of  Ordnance,  U.  S-  Army.  Illustrated,  second  edi- 
tion, 410,  cloth 3  oo 

MICHAELIS.  The  Le  Boulenge  Chronograph,  with 
three  Lithograph  folding  plates  of  illustrations.  By 
Brevet  Captain  O.  E.  Michaelis,  First  Lieutenant 
Ordnance  Corps,  U.  S.  Army,  410,  cloth 3  oo 

ENGINEERING  FACTS  AND  FIGURES  An 
Annual  Register  of  Progress  in  Mechanical  Engineer- 
ing and  Construction,  for  the  years  1863,  64,  65,  66, 
67,  68.  Fully  illustrated,  6  vols.  i8mo,  cloth,  $2.50 
per  vol.,  each  volume  sold  separately 

HAMILTON.  Useful  Information  for  Railway  Men. 
Compiled  by  W.  G.  Hamilton,  Engineer.  Fifth  edi- 
tion, revised  and  enlarged,  562  pages  Pocket  form. 
Morocco,  gilt..,.,,,. , 2  oo 


1).  VAN  NOSTRAND  S  PUBLICATIONS. 


STUART.  The  Civil  and  Military  Engineers  of  Amer- 
ica. By  Gen.  C.  B.  Stuart.  With  9  finely  executed 
portraits  of  eminent  engineers,  and  illustrated  by 
engravings  of  some  of  the  most  important  works  con- 
structed in  America.  8vo,  cloth $5  bo 

STONEY.  The  Theory  of  Strains  in  Girders  .and  simi- 
lar structures,  with  observations  on  the  application  of 
Theory  to  Practice,  and  Tables  of  Strength  and  other 
properties  of  Materials.  By  Bindon  B.  Stoney,  B.  A. 
New  and  revised  edition,  enlarged,  with  numerous 
engravings  on  wood,  by  Oldham.  Royal  8vo,  664 
pages.  Complete  in  one  volume.  8vo,  cloth 12  50 

SHREVE.  A  Treatise  on  the  Strength  of  Bridges  and 
Roofs.  Comprising  the  determination  of  Algebraic 
formulas  for  strains  in  Horizontal,  Inclined  or  Rafter, 
Triangular,  Bowstring,  Lenticular  and  other  Trusses, 
from  fixed  and  moving  loads,  with  practical  applica- 
tions and  examples,  for  the  use  of  Students  and  Engi- 
neers. By  Samuel  H.  Shreve,  A.  M. ,  Civil  Engineer. 
87  wood  cut  illustrations.  8vo,  cloth 5  oo 

MERRILL.  Iron  Truss  Bridges  for  Railroads.  The 
method  of  calculating  strains  in  Trusses,  with  a  care- 
ful comparison  of  the  most  prominent  Trusses,  in 
reference  to  economy  in  combination,  etc. ,  etc.  By 
Brevet  Col.  William  E.  Merrill,  U  S.  A.,  Major 
Corps  of  Engineers,  with  nine  lithographed  plates  of 
Illustrations.  410,  cloth... 500 

WHIPPLE.  An  Elementary  and  Practical  Treatise  on 
Bridge  Building.  An  enlarged  and  improved  edition 
of  the  author's  original  work.  By  S.  Whipple,  C  E., 
inventor  of  the  Whipple  Bridges,  &c.  Illustrated 
8vo,  cloth 4  oo 

THE  KANSAS  CITY  BRIDGE.  With  an  account 
of  the  Regimen  of  the  Missouri  River,  and  a  descrip- 
tion of  the  methods  used  for  Founding  in  that  River. 
By  O.  Chanute,  Chief  Engineer,  and  George  Morri- 
son, Assistant  Engineer.  Illustrated  with  five  litho- 
graphic views  and  twelve  plates  of  plans.  4to,  cloth.  6  oo 


D.  VAST  NOSTRAND'S  PUBLICATIONS. 


MAC  CORD.  A  Practical  Treatise  on  the  Slide  Valve 
by  Eccentrics,  examining  by  methods  the  action  of  the 
Eccentric  upon  the  Slide  Valve,  and  explaining  the 
Practical  processes  of  laying  out  the  movements, 
adapting  the  valve  for  its  various  duties  in  the  steam 
engine.  For  the  use  of  Engineers,  Draughtsmen, 
Machinists,  and  Students  of  Valve  Motions  in  gene 


l.  By  C.  W.  Mac  Cord,  A,  M.  ,  Professor  of  Me- 
hanical Drawing,  Stevens'  Institute  of  Technology, 
Hoboken,  N.  J.  Illustrated  by  8  full  page  copper- 


. 
plates.    4to,  cloth  ................................  $400 

KIRK  WOOD.  Report  on  the  Filtration  of  River 
Waters,  for  the  supply  of  cities,  as  practised  in 
Europe,  made  to  the  Board  of  Water  Commissioners 
of  the  City  of  St.  Louis.  By  James  P-  Kirkwood. 
Illustrated  by  30  double  plate  engravings.  4to,  cloth,  1  5  oo 

PLATTNER.  Manual  of  Qualitative  and  Quantitative 
Analysis  with  the  Blow  Pipe.  From  the  last  German 
edition,  revised  and  enlarged.  By  Prof.  Th.  Richter, 
of  the  Royal  Saxon  Mining  Academy.  Translated 
by  Prof.  H.  B.  Cornwall,  Assistant  in  the  Columbia 
School  of  Mines,  New  York  assisted  by  John  H. 
Caswell.  Illustrated  with  87  wood  cuts*  and  one 
lithographic  plate.  Second  edition,  revised,  560 
pages,  8vo,  cloth  .................................  7  50 

PLYMPTON.  The  Blow  Pipe.  A  Guide  to  its  Use 
in  the  Determination  of  Salts  and  Minerals.  Com- 
piled from  various  sources,  by  George  W.  Plympton, 
C  E.  A.  M.,  Professor  of  Physical  Science  in  the 
Polytechnic  Institute,  Brooklyn,  New  York,  J2mo, 
cloth  ............................................  i  so 

PYNCHON.   Introduction  to  Chemical  Physics,  design- 
ed for  the  use   of  Academies,  Colleges  and  High 
Schools.     Illustrated  with  numerous  engravings,  and 
containing  copious  experiments   with  directions  for 
preparing  them.      By  Thomas   Ruggles    Pynchon, 
M.  A.,  Professor  of  Chemistry  and  the  Natural  Sci- 
ences, Trinity  College,  Hartford     New  edition,  re- 
vised and  enlarged,  and  illustrated  by  269  illustrations 
onwood.     Crown,  8vo.  cloth  ......................     3  °° 

9 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 


operation  of  the  authors.  By  William  R.  Nichols, 
Professor  of  Chemistry  in  the  Massachusetts  Insti- 
tute of  Technology  Illustrated,  12010,  cloth $i  50 

RAMMELSBERG.  Guide  to  a  course  of  Quantitative 
Chemical  Analysis,  especially  of  Minerals  and  Fur- 
nace, Products.  Illustrated  by  Kxamples  By  C.  F. 
Ramroalsberg.  Translated  by  J.  Towler,  M.  D. 
8vo,  cloth 2  23 

EGLESTON.  Lectures  on  Descriptive  Mineralogy,  de- 
livered at  the  School  of  Mines,  Columbia  College. 
By  Professor  T.  Egleston.  Illustrated  by  34  Litho- 
graphic Plates.  8vo,  cloth 450 

JACOB.  On  the  Designing  and  Construction  of  Storage 
Reservoirs,  with  Tables  and  Wood  Cuts  representing 
Sections,  &c.,  i8mo,  boards 50 

WATT'S  Dictionary  of  Chemistry.      New  and  Revised     - 
edition  complete  in  6  vols,   8vo  cloth,  $62.00.    Sup-     * 
1  plementary  volume  sold  separately.     Price,  cloth. . .    9  oo 

RANDALL.  Quartz  Operators  Hand-Book.  By  P.  M. 
Randall.  New  edition,  revised  and  enlarged,  fully 
illustrated,  izmo,  cloth  200 

SILVERSMITH.  A  Practical  Hand-Book  for  Miners, 
Metallurgists,  and  Assayers,  comprising  the  most  re- 
cent improvements  in  the  disintegration  amalgama- 
tion, smelting,  and  parting  of  the  1  recious  ores,  with 
a  comprehensive  Digest  of  the  Mining  Laws.  Greatly 
augmented,  revised  and  corrected.  By  Julius  Silver- 
smith. Fourth  edition.  Profusely  illustrated,  izmo, 
cloth 3  °» 

THE  USEFUL  METALS  AND  THEIR  ALLOYS, 
including  Mining  Ventilation,  Mining  Jurisprudence, 
and  Metallurgic  Chemistry  employed  in  the  conver- 
sion of  Iron,  Copper,  Tin,  Zinc,  Antimony  and  Lead 
ores,  with  their  applications  to  the  Industrial  Arts. 
By  Scoffren,  Truan,  Clay,  Oxland,  Fairbairn,  and 

others.    Fifth  edition,  half  calf ,,, 3  73 

10 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

JOYNSON.  The  Metals  used  in  construction,  Iron, 
Steel,  Bessemer  Metal,  etc.,  etc.  By  F.  H.  Joynsorw 
Illustrated,  12010,  doth $o  7 j 

VON  COTTA.  Treatise  on  Ore  Deposits.  By  Bern- 
hard  Von  Cotta,  Professor  of  Geology  in  the  Royal 
School  of  Mines,  Freidberg,  Saxony.  Translated 
from  the  second  German  edition,  by  Frederick 
Prime,  Jr.,  Mining  Engineer,  and  revised  by  the  au- 
thor, with  numerous  illustrations.  8vo,  cloth. 4  oo 

GREENE.  Graphical  Method  for  the  Analysis  of  Bridge 
Trusses,  extended  to  continuous  Girders  and  Draw 
Spans.  By  C.  K.  Greene,  A.  M.,  Prof,  of  Civil  Engi- 
neering, University  of  Michigan.  Illustrated  by  3 
folding  plates,  8vo,  cloth 300 

BELL.  Chemical  Phenomena  of  Iron  Smelting.  An 
experimental  and  practical  examination  of  the  cir- 
cumstances which  determine  the  capacity  of  the  Blast 
Furnace,  The  Temperature  of  the  air,  and  the 
proper  condition  of  the  Materials  to  be  operated 
upon.  By  1.  Lowthian  Bell.  8vo,  cloth 6  «o 

ROGERS.  The  Geology  of  Pennsylvania.  A  Govern- 
ment survey,  with  a  general  view  of  the  Geology  of 
the  United  States,  Essays  on  the  Coal  Formation  and 
its  Fossils,  and  a  description  of  the  Coal  Fields  of 
North  America  and  Great  Britain.  By  Henry  Dar- 
win Rogers,  late  State  Geologist  of  Pennsylvania, 
Splendidly  illustrated  with  Plates  and  Engravings  in 
the  text  3  vols.,  410,  cloth,  with  Portfolio  of  Maps.  30  oo 

BURGH.  Modern  Marine  Engineering,  applied  to 
Paddle  and  Screw  Propulsion.  Consisting  of  36 
colored  plates,  259  Practical  Wood  Cut  Illustrations, 
and  403  pages  ol  descriptive  matter,  the  whole  being 
an  exposition  of  the  present  practice  of  James 
Watt  &  Co.,  J.  &  G.  Rennie,  R.  Napier  &  Sons, 
and  other  celebrated  firms,  by  N.  P.  Burgh,  Engi- 
neer, thick  4to,  vol.,  doth,  $25.00 ;  half  mor. 30  °° 

CHURCH.  Notes  of  a  Metallurgical  Journey  in  Europe. 

By  J,  A.  Church,  Engineer  of  Mines,  8vo,  cloth.. ...  2  oo 

11 


IX  VAN  NOSTRAND'B  PUBLICATIONS. 

BOURNE.  Treatise  on  the  Steam  Engine  in  its  various 
applications  to  Mines,  Mills,  Steam  Navigation, 
Railways,  and  Agriculture,  with  the  theoretical  in- 
vestigations respecting  the  Motive  Power  of  Heat, 
and  the  proper  proportions  of  steam  engines.  Elabo- 
rate tables  of  the  right  dimensions  of  every  part,  and 
Practical  Instructions  for  the  manufacture  and  man- 
agement of  every  species  of  Engine  in  actual  use. 
By  John  Bourne,  being  the  ninth  edition  of  "  A 
Treatise  on  the  Steam  Engine,"  by  the  "Artizan 
Club."  Illustrated  by  38  plates  and  546  wood  cuts. 
4to,  cloth ,..$15  oo 

STUART.      The  Naval  Dry  Docks  of  the   United  , 
Slates.   By  Charles  B.  Stuart  late  Engineer-in-Chief 
of  the  U.  S.  Navy.    Illustrated  with  24  engravings 
on  steel    Fourth  edition,  cloth 600 

ATKINSON.     Practical  Treatises  on  the  Gases  met 

with  in  Coal  Mines.     i8mo,  boards 50 

FOSTER.      Submarine  Blasting  in    Boston    Harbor, 
Massachusetts.      Removal  of  Tower  and    Corwin     < 
Rocks.    By  J.  G.  Foster,  Lieut -Col.  of  Engineers, 
U.    S.  Army.    Illustrated  with  seven  plates,  410, 
cloth 3  50 

BARNES  Submarine  Warfare,  offensive  and  defensive, 
including  a  discussion  of  the  offensive  Torpedo  Sys- 
tem, its  effects  upon  Iron  Clad  Ship  Systems  and  in- 
fluence upon  future  naval  wars.  By  Lieut. -Com- 
mander J.  S.  Barnes,  U.  S.  NM  with  twenty  litho- 
graphic plates  and  many  wood  cuts.  8vo,  cloth. . .  „ .  5  oo 

HOLLEY.     A  Treatise  on  Ordnance  and  Armor,  em- 
bracing descriptions,   discussions,   and  professional 
opinions  concerning  the  materials,  fabrication,  re- 
quirements, capabilities,  and  endurance  of  European 
and  American  Guns,  for  Naval,  Sea  Coast,  and  Iron 
Clad  Warfare,  and  their  Rifling,  Projectiles,  and 
Breech-Loading;  also,  results  of  experiments  against 
armor,  from  official  records,  with  an  appendix  refer-    f 
ring  to  Gun  Cctton,  Hooped  Guns,  etc.,  etc.    By    f 
Alexander  L.  Holley,  B.  P.,  948  pages,  493  engrav- 
ings, and  147  Tables  of  Results,  etc.,  8vo,  half  roan.  10  oo 
12 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 


SIMMS.  A  Treatise  on  the  Principles  and  Practice  of 
Levelling,  showing  its  application  to  purposes  of 
Railway  Engineering  and  the  Construction  of  Roads, 
&c.  By  Frederick  W.  Simms,  C.  E.  From  the  5th 
London  edition,  revised  and  corrected,  with  the  addi- 
tion of  Mr.  Laws's  Practical  Examples  for  setting 
out  Railway  Curves.  Illustrated  with  three  Litho- 
graphic plates  and  numerous  wood  cuts.  8vo,  cloth.  $2  50 

BURT.  Key  to  the  ^lar  Compass,  and  Surveyor's. 
Companion ;  comprising  all  the  rules  necessary  for 
use  in  the  field ;  also  description  of  the  Linear  Sur- 
reys and  Public  Land  System  of  the  United  States, 
Notes  on  the  Barometer,  suggestions  for  an  outfit  for 
a  survey  of  four  months,  etc.  By  W.  A.  Burt,  U.  S. 
Deputy  Surveyor.  Second  edition.  Pocket  book 
form,  tuck < 3  50 

THE  PLANE  TABLE.  Its  uses  in  Topographical 
Surveying,  from  the  Papers  of  the  U.  S.  Coast  Sur- 
vey. Illustrated,  8vo,  cloth 200 

"  This  worK  gives  a  description  of  the  Plane  Table,  employed  at  th« 
U.  S.  Coast  Surrey  office,  and  the  manner  of  using  it." 

JEFFER'S.  Nautical  Surveying.  By  W.  N.  Jefiers, 
Captain  U.  S.  Navy.  Illustrated  with  9  copperplates 
and  31  wood  cut  illustrations.  8vo,  cloth. 5  oo 

CHAUVENET.  New  method  of  correcting  Lunar  Dis- 
tances, and  improved  method  of  Finding  the  error 
and  rate  of  a  chronometer,  by  equal  altitudes.  By 
W.  Chauvenet,  LL.D.  8vo,  doth 2  oo 

BRUNNOW.  Spherical  Astronomy.  By  F.  Brunnow, 
Ph.  Dr.  Translated  by  the  author  from  the  second 
German  edition.  8vo,  cloth 6  yo 

PEIRCE.  System  of  Analytic  Mechanics.  By  Ben- 
jamin Peirce.  4to,  cloth 10  oo 

COFFIN.  Navigation  and  Nautical  Astronomy.  Pre- 
pared for  the  use  of  the  U.  S.  Naval  Academy.  By 
Prof.  J.  H.  C.  Coffin.  Fifth  edition.  52  wood  cut  illus- 
trations, izmo,  cloth , 3  50 

13 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

CLARK.  Theoretical  Navigation  and  Nautical  Astron- 
omy. By  Lieut  Lewis  Clark,  U.  S.  N.  Illustrated 
with  41  wood  cuts.  8vo,  cloth $3  oo 

HASKINS.  The  Galvanometer  and  its  Uses.  A  Man- 
tial  for  Electricians  and  Students.  By  C.  H.  Has- 
kins.  i2mo,  pocket  form,  morocco.  (In  press) 

GOUGE.  New  System  of  Ventilation,  which  has  been 
thoroughly  tested,  under  the  patronage  of  many  dis- 
tinguished persons.  By  Henry  A.  Gouge.  With 
many  illustrations.  8vo,  cloth a  oo 

BECK  WITH.  Observations  on  the  Materials  and 
Manufacture  of  Terra-Cotta,  Stone  Ware,  Fire  Brick, 
Porcelain  and  Encaustic  Tiles,  with  remarks  on  the 
products  exhibited  at  the  London  International  Exhi- 
bition, 1871.  By  Arthur  Beckwith,  C.  E.  8vo, 
paper 60 

MORFIT.  A  Practical  Treatise  on  Pure  Fertilizers,  and 
the  chemical  conversipn  of  Rock  Guano,  Marlstones, 
Coprolites.  and  the  Crude  Phosphates  of  Lime  and 
Alumina  generally,  into  various  valuable  products. 
By  Campbell  Morfit,  M.D.,  with  28  illustrative  plates, 

8VO,  Cloth 2090 

BARNARD.  Tne  Metric  System  of  Weights  and 
Measures.  An  address  delivered  before  the  convoca- 
tion of  the  University  of  the  State  of  New  York,  at 
Albany,  August,  1871.  By  F.  A.  P.  Barnard,  LL.D., 
President  of  Columbia  College,  New  York.  Second 
edition  Jrom  the  revised  edition,  printed  for  the  Trus- 
tees of  Columbia  College.  Tinted  paper,  8vo,  cloth  3  oo 

...  Report  on  Machinery  and  Processes  on  the  In- 
dustrial Arts  and  Apparatus  of  the  Exact  Sciences, 
By  F.  A.  P.  Barnard,  LL.D.  Paris  Universal  Ex* 
position,  1867.  Illustrated,  8vo,  cloth. 5  ot 

ALLAN.  Theory  of  Arches.  By  Prof.  W.  Allan,  for- 
merly of  Washington  &  Lee  University,  1 8mo,  b'rds  50 

14 


r>»  VAN  NOSTRAND'S  PUBLICATIONS. 


MYER.  Manual  of  Signals,  for  the  use  of  Signal  officers 
in  the  Field,  and  for  Military  and  Naval  Students, 
Military  Schools,  etc.  A  new  edition  enlarged  and 
illustrated  By  Brig.  General  Albert  J.  Myer,  Chief 
Signal  Officer  of  the  army,  Colonel  of  the  Signal 
Corps  during  the  War  of  the  Rebellion.  i2mo,  48 
plates,  full  Roan $5  oo 

WILLIAMSON.  Practical  Tables  in  Meteorology  and 
Hypsometry,  in  connection  with  the  use  of  the  Bar- 
ometer. By  CoL  R.  S.  Williamson,  U.  S.  A.  410, 
cloth. , 2  50 

CLEVENGER.  A  Treatise  on  the  Method  of  Govern- 
ment Surveying,  as  prescribed  by  the  U.  S.  Congress 
and  Commissioner  of  the  General  Land  Office,  with 
complete  Mathematical,  Astronomical  and  Practical 
Instructions  for  the  Use  of  the  United  States  Sur- 
veyors in  the  Field.  By  S.  R.  Clevenger;  Pocket 
Book  Form,  Morocco 2  50 

PICKERT  AND  METCALF.     The  Art  of  Graining. 


.autifully 

42  tinted  plates  of  the  various  woods  used  in  interior 
finishing.    Tinted  paper,  410,  cloth 10  oo 

HUNT.  Designs  for  the  Gateways  of  the  Southern  En- 
trances to  the  Central  Park.  By  Richard  M.  Hunt. 
With  a  description  of  the  designs.  4to.  cloth 5  oo 

LAZELLE.  One  Law  in  Nature.  By  Capt.  H.  M. 
Lazelle,  U.  S.  A.  A  new  Corpuscular  Theory,  com- 
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its  Multiple  Atom  Constitution,  applied  to  the  Physi- 
cal Affections  or  Modes  of  Energy.  i2mo,  cloth. ..  i  50 

CORFIELD.  Water  and  Water  Supply.  By  W.  H. 
Corfield,  M.  A.  M,  D.,  Professor  of  Hygiene  and 
Public  Health  at  University  College,  London.  i8mo, 
boards 50 

15 


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BOYNTON.  History  of  West  Point,  its  Military  Im- 
portance during  the  American  Revolution,  and  the 
Origin  and  History  of  the  U.  S.  Military  Academy. 
By  Bvt  Major  C.  E.  Boynton,  A.M.,  Adjutant  of  the 
Military  Academy.  Second  edition,  416  pp.  Syo. 
printed  on  tinted  paper,  beautifully  illustrated  witfy 
36  maps  and  fine  engravings,  chiefly  from  photo- 
graphs taken  on  the  spot  by  the  author.  Extra 
cloth $3  s9 

WOOD.  West  Point  Scrap  Book,  being  a  collection  of 
Legends,  Stories,  Songs,  etc-,  of  the  U.  S.  Military 
Academy.  By  Lieut.  O.  E.  Wood,  U.  S.  A.  Illus- 
trated by  69  engravings  and  a  copperplate  map. 
Beautifully  printed  on  tinted  paper.  8vo,  cloth 5  oo 

WEST  POINT  LIFE.  A  Poem  read  before  the  Dia- 
lectic Society  of  the  United  States  Military  Academy. 
Illustrated  with  Pen-and-ink  Sketches.  By  a  Cadet. 
To  which  is  added  the  song,  "  Benny  Havens,  oh  I" 
oblong  Svo,  21  full  page  illustrations,  cloth. 2  50 

GUIDE  TO  WEST  POINT  and  the  U.  S.  Military 
Academy,  with  maps  and  engravings,  i8mo,  blue 
cloth,  flexible .,..  z  oo 

HENRY.  Military  Record  of  Civilian  Appointments  in 
the  United  States  Army,  By  Guy  V.  Henry,  Brevet 
Colonel  and  Captain  First  United  States  Artillery, 
Late  Colonel  and  Brevet  Brigadier  General,  United 
States  Volunteers.  Vol.  x  now  ready.  Vol.  2  in 
press.  Svo,  per  volume,  cloth 500 

HAMERSLY.  Recprds  of  Living  Officers  of  the  U. 
S.  Navy  and  Marine  Corps.  Compiled  from  official 
sources.  By  Lewis  B.  Hamersly,  late  Lieutenant 
U.  S.  Marine  Corps.  Revised  edition,  Svo,  cloth...  5  oo 

MOORE.  Portrait  Gallery  of  the  War.  Civil,  Military 
and  Naval.  A  Biographical  record,  edited  by  Frank 
Moore.  60  fine  portraits  on  steel.  Royal  Svo, 
cloth 6  oo 

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PRESCOTT.  Outlines  of  Proximate  Organic  Analysis, 
for  the  Identification,  Separation,  and  Quantitative 
Determination  of  the  more  commonly  occurring  Or. 
ganic  Compounds.  By  Albert  B.  Prescott,  Professor 
of  Chemistry,  University  of  Michigan,  12010,  doth...  x  75 

PRESCOTT.  Chemical  Examination  of  Alcoholic  Li- 
quors. A  Manual  of  the  Constituents  of  the  Distilled 
Spirits  and  Fermented  Liquors  of  Commerce,  and 
their  Qualitative  and  Quantitative  Determinations. 
By  Albert  B.  Prescott,  12010,  cloth i  50 

BATTERSHALL.  Legal  Chemistry.  A  Guide  to  the 
Detection  of  Poisons,  Falsification  of  Writings,  Adul- 
teration of  Alimentary  and  Pharmaceutical  Substan- 
ces; Analysis  of  Ashes,  and  examination  of  Hair, 
Coins,  Arms  and  Stains,  as  applied  to  Chemical  Ju- 
risprudence, for  the  Use  of  Chemists,  Physicians, 
Lawyers,  Pharmacists  and  Experts  Translated  with 
additions,  including  a  list  of  books  and  Memoirs  on 


Texicology,  etc.  from  the  French  of  A.  Naquet  By 
J.  P.  Battershall,  Ph.  D.  with  a  preface  by  C.  F. 
Chandler,  Ph.  D-,  M.  D,,  L.  L.  D.  i2mo,  cloth. . . . 

:CUL  LOCH.  Elementary  Treatise  on 
ical  Theory  of  Heat,  and  its  applicatio 
Steam  Engines.  By  R.  S.  McCulloch,  8 


McCULLOCH.     Elementary  Treatise  on  the  Mechan- 

ition  to  Air  and 
,  8vo,  cloth....    

AXON.  The  Mechanics  Friend ;  a  Collection  .of  Re- 
ceipts and  Practical  Suggestions  Relating  to  Aqua- 
ria— Bronzing— Cements— Drawing— Dyes—  Electri- 
city— Gilding — Glass  Working — Glues — Horology — 
Lacquers — Locomotives — Magnetism — Metal- Work- 
ing—Modelling—  P  holography-  Pyrotechy— Railways 
— Solders — Steam  Engine — Telegraphy — Taxidermy 
—  Varnishes  —  Water-Proofing  and  Miscellaneous 
Tools, — Instruments,  Machines  &nd  Processes  con- 
nected with  the  Chemical  and  Mechanics  Arts ;  with 
numerous  diagrams  and  wood  cuts.  Edited  by  Wil- 
liam E.  A.  Axon.  Fancy  doth 150 

17 


D.  VAN  NOSTRAND  S  PUBLICATIONS. 

ERNST.  Manual  of  Practical  Military  Engineering,  Pre- 
pared for  the  use  of  the  Cadets  of  the  U.  S.  Military 
Academy,  and  for  Engineer  Troops.  By  Capt.  O.  H. 
Ernst,  Corps  of  Engineers,  Instructor  in  Practical 
Military  Engineering,  U.  S.  Military  Academy.  193 
wood  cuts  and  3  lithographed  plates,  izmo,  cloth..  500 

BUTLER.  Projectiles  and  Rifled  Cannon.  A  Critical 
Discussion  of  the  Principal  Systems  of  Rifling  and 
Projectiles,  with  Practical  Suggestions  for  their  Im- 
provement, as  embraced  in  a  Report  to  the  Chief  of 
Ordnance,  U.  S.  A.  By  Capt.  John  S.  Butler,  Ord- 
nance Corps,  U-  S.  A.  36  plates,  4to,  cloth 7  50 

BLAKE.  Report  upon  the  Precious  Metals :  Being  Sta- 
tistical Notices  of  the  principal  Gold  and  Silver  pro- 
ducing regions  of  the  World,  Represented  at  the 
Paris  Universal  Exposition.  By  William  P.  Blake, 
Commissioner  from  the  State  of  California.  8vo,  cloth  2  oo 

TONER.  Dictionary  of  Elevations  and  Climatic  Regis- 
ter of  the  United  States.  Containing  in  addition  to 
Elevations,  the  Latitude,  Mean,  Annual  Temperature, 
and  the  total  Annual  Rain  fall  of  many  localities;  with 
a  brief  introduction  on  the  Orographic  and  Physical 
Peculiarities  of  North  America.  By  J.  M.  Toner, 
M.  D.  8vo,  cloth 3  75 

MOWBRAY.  Tri-Nitro  Glycerine,  as  applied  in  the 
Hoosac  Tunnel,  and  to  Submarine  Blasting,  Torpe- 
does, Quarrying,  etc.  Being  the  result  of  six  year's 
observation  and  practice  during  the  manufacture  of 
five  hundred  thousand  pounds  of  this  explosive  Mica, 
Blasting  Powder,  Dynamites;  with  an  account  of  the 
various  Systems  of  Blasting  by  Electricity,  Priming 
Compounds,  Explosives,  etc.,  etc.  By  George  M. 
Mowbray,  Operative  Chemist,  with  thirteen  illustra- 
tions, tables  and  appendix.  Third  Edition.  Re- 
written. 8vo.  cloth « 3  oo 

18 


THE   VAN  XOSTRAND  SCIENCE  SERIES. 


No.  60.— STRENGTH  OF  WROUGHT-IRON  BRIDGE  MEM- 
BERS. By  S.  W.  Robinson,  C.E. 

No.  61. -POTABLE  WATER  AND  THE  DIFFERENT 
METHODS  OF  DETECTING  IMPURITIES.  By 
Charles  W.  Folkhard. 

No.  6-2.— THE  THEORY  OF  THE  GAS  -  ENGINE.  By 
Dougald  Clerk.  Second  edition.  With  additional 
matter.  Edited  by  F.  E.  Idell,  M.E. 

No.  63.— HOUSE  DRAINAGE  AND  SANITARY  PLUMB- 
ING. By  W.  P.  Gerhard.  Fourth  edition.  Re- 
vised. 

No.  64.— ELECTRO-MAGNETS.  By  Th.  du  Moncel.  3d  re- 
vised edition. 

No.  65.-POCKET  LOGARITHMS  TO  FOUR  PLACES  OF 
DECIMALS. 

No.  66.— DYNAMO-ELECTRIC    MACHINERY.      By    S.    P. 

Thompson.    With  notes  by   F.   L.    Pope.    Third 

edition. 
Xo.  67.— HYDRAULIC  TABLES  BASED  ON    "KUTTER'S 

FORMULA."    By  P.  J.  Flynn. 
No.  68. -STEAM-HEATING.      By  Robert    Briggs.      Second 

edition,  revised,  with  additions  by  A.  R.  Wolff. 
No.  69.— CHEMICAL    PROBLEMS.     By    Prof    J.   C.    Foye. 

Second  edition,  revised  and  enlarged. 
No.  70.— EXPLOSIVES    AND    EXPLOSIVE    COMPOUNDS. 

By  M.  Bertholet. 
No.  71.— DYNAMIC  ELECTRICITY.     By  John  Hopkinson, 

J.  A.  Schoolbred,  and  R.  E.  Day. 
No.  72.— TOPOGRAPHICAL    SURVEYING.     By  George  J. 

Specht,  Prof.  A.  S.  Hardy,  John  B.  McMaster.  and 

H.  F.  Walling. 
No.  73.— SYMBOLIC  ALGEBRA:  OR,  THE  ALGEBRA  OF 

ALGEBRAIC  NUMBERS.     By  Prof.  W.  Cain. 
No.  74.— TESTING   MACHINES  :  THEIR  HISTORY,  CON- 
STRUCTION, AND  USE.     By  Arthur  V.  Abbott. 

No.  75.— RECENT  PROGRESS  IN  DYNAMO-ELECTRIC 
MACHINES.  Being  a  Supplement  to  Dynamo- 
Electric  Machinery.  By  Prof.  Sylvanus  P. 
Thompson. 

No.  76.— MODERN  REPRODUCTIVE  GRAPHIC  PRO- 
CESSES. By  Lieut.  James  S.  Pettit,  U.S.A. 

No.  77.-STADIA  SURVEYING.  The  Theory  of  Stadia 
Measurements.  By  Arthur  Winslow. 

No.  78.— THE  STEAM-ENGINE  INDICATOR  AND  ITS 
USE.  By  W.  B.  Le  Van. 

No.  79.-THK  FIGURE  OF  THE  EARTH.  By  Frank  C. 
Roberts.  C  K 

No.  80. -HEALTHY  FOUNDATIONS  FOR  HOUSES.  By 
Glenn  Brown. 


THIS  BOOK  IS  DUB  ON  THE  LAST  DATE 
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AN     INITIAL    FINE    OF    25    CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
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FEB    5  1933 
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i  r\    vj  r  o  I  ^j 

THE  rRAND  SCIENCE  SERIES. 


No.  100.-HOW  TO  BECOME  AN  ENGINEER,  or  the  Theo- 
retical and  Practical  Training  necessary  in  fitting 
for  the  duties  of  the  Civil  Engineer.  By  Prof. 
Geo.  W.  Plympton. 

No.  101.— THE  SEXTANT,  and  other  Reflecting  Mathemati- 
cal Instruments.  With  Practical  Hints  for  their 
adjustment  and  use.  By  F.  R.  Brainard,  U.  S. 
Navy. 

No.  102.— THE     GALVANIC     CIRCUIT     INVESTIGATED 
MATHEMATICALLY.    By  Du.  G.  S.  Ohm,  Ber- 
lin, 18^7.     Translated  by  William  Francis.     With 
Preface   and    Notes  by  the  Editor,   Thoma 
Lockwood,  M.I.E.E. 

No.  103.— THE      MICROSCOPICAL     EXAMINATION     OF 
POTABLE    WATER.     Witn  Diagrams.     Bv  ' 
W.  Rafter. 


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